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Thread: Mathematic of Language

  1. #1 Mathematic of Language 
    Forum Freshman Eldritch's Avatar
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    To start with, I have no idea where I should be posting this. Mathematics seemed the most applicable. Any help in a better category would be appreciated.

    Anyway, I remember hearing awhile ago about a method that could determine if a set of noises, symbols, or something of the sort comprised a language. By counting the number of times and vocalization or somesuch appeared in a given time, and then graphing the frequency of each item, you could tell if you had a language or not. Each item was one dot on the X axis, and the frequency of its use was on the Y axis. If what before was truly a language, the graph would make a right triangle.

    I can't quite remember where I heard this from, or what it is called. Does anyone have any ideas?


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    so basically determination of an imaginary concept


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    Brassica oleracea Strange's Avatar
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    I'm sure some sort of statistical analysis like that could be done of natural languages. I haven't read of anything specifically like that, but I wouldn't be surprised if the distribution of phonemes or written symbols was easily distinguishable from random.

    In fact, as I type this, I have a vague recollection of having read something about the distribution of sounds and/or morphemes following a power law...
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    Quote Originally Posted by fiveworlds View Post
    so basically determination of an imaginary concept
    You think language is an imaginary concept? That might explain the nature of some of your posts.
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    But surely you could mathematically graph practically any sounds. These sounds creating a language would be entirely a human invention think how many languages there are thousands some reusing the same symbols and sounds. Its just maths we assign meanings to things we always have.
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    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by fiveworlds View Post
    But surely you could mathematically graph practically any sounds. These sounds creating a language would be entirely a human invention think how many languages there are thousands some reusing the same symbols and sounds. Its just maths
    Exactly, but what Eldritch is referring to would imply that there is a consistent pattern in human language that distinguishes it from random sounds or symbols.

    I would not be surprised if this were true. After all, all human languages are based on the same mental apparatus and have, therefore a number of things in common. The distribution of phonemes/morphemes could well be one of these universals. I would love to know more....
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  8. #7  
    Brassica oleracea Strange's Avatar
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    I have just found this, for example: http://www.dmi.unict.it/~faro/papers...ence/faro1.pdf

    I will keep looking ...
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    but consider this you apply what we know. A language is a means to communicate therfore it need some regularity. This statement for example the sky is blue here you can see we have a few elements the sky is blue ,object(sky)=blue now everytime you want to make an object in this language you must use object() therefore it repeats wheras sky is a variable so it wont. There is no point in having multiple words for object abc etc but that doesnt mean a possiblity doesnt exsist where you could call object, hds or something else and have multiple different meanings for object based on the variable you use. The correlation between maths and sound is the one that we define
    Last edited by fiveworlds; May 5th, 2013 at 08:15 PM.
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  10. #9  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by fiveworlds View Post
    but consider this you apply what we know. A language is a means to communicate therfore it need some regularity. This statement for example the sky is blue here you can see we have a few elements the sky is blue ,object(sky)=blue now everytime you want to make an object in this language you must use object() therefore it repeats wheras sky is a variable so it wont. There is no point in having multiple words for object abc etc but that doesnt mean a possiblity doesnt exsist where you could call object, hds or something else and have multiple different meanings for object based on the variable you use. The correlation between maths and sound is the one that we define
    I was going to make a detailed reply to this but it demonstrates so little knowledge of linguistics that I can't be bothered.
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    kinda funny its not as if I would not like to learn loads of language rather its difficult to find time to learn them all. im assuming you can speak every language right? nor can I see how you can expect a deaf person or somebody with a speech impediment to be able to replicate the exact right sound within a certain range
    Last edited by fiveworlds; May 6th, 2013 at 09:12 AM.
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    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by fiveworlds View Post
    but consider this you apply what we know. A language is a means to communicate therfore it need some regularity. This statement for example the sky is blue here you can see we have a few elements the sky is blue ,object(sky)=blue now everytime you want to make an object in this language you must use object() therefore it repeats wheras sky is a variable so it wont. There is no point in having multiple words for object abc etc but that doesnt mean a possiblity doesnt exsist where you could call object, hds or something else and have multiple different meanings for object based on the variable you use.
    OK, let's take you "sky is blue" example. There are an infinite number of sentences of this form, some with "sky" as the subject and some with "blue" as the predicate. There are many other sentences where "sky" or "blue" could occur. I suspect the sentence "the sky is blue" is more frequent than "the frangipani is odoriferous". Therefore, the suggestion is, we could detect a difference between random strings (where one would expect all symbols to occur with equal frequency) and natural language (where some symbols will be more frequent than others in a predictable way).

    I don't know what "object()" is supposed to mean but is is not part of the language.

    The correlation between maths and sound is the one that we define
    The maths was supposed to be used to look for correlations or patterns in language.
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    Quote Originally Posted by fiveworlds View Post
    kinda funny its not as if I would not like to learn loads of language rather its difficult to find time to learn them all. im assuming you can speak every language right?
    None of that is in the least bit relevant.

    nor can I see how you can expect a deaf person or somebody with a speech impediment to be able to replicate the exact right sound within a certain range
    I'm sure the same sort of correlations or distribution of symbols exist in sign languages as in spoken or written languages.
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    Forum Freshman Eldritch's Avatar
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    I think what I was talking about is similar to frequency analysis (used in cryptanalysis) being applied to an unknown situation.
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    my way of thinking about it is assume something only operates on a certain range of frequencies. Now things are assigned to these frequencies the meaning changes but you only ever operate within a finite limited range one could assume therefore that everything made on this is therfore constrained to a small range no matter what you assign. Easy right?
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  16. #15  
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    Quote Originally Posted by Eldritch View Post
    I think what I was talking about is similar to frequency analysis (used in cryptanalysis) being applied to an unknown situation.
    That is exactly the sort of thing I am thinking of. I assume it applies in a similar way to individual letters (or phonemes), morphemes and words.
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  17. #16  
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    Quote Originally Posted by fiveworlds View Post
    my way of thinking about it is assume something only operates on a certain range of frequencies. Now things are assigned to these frequencies the meaning changes but you only ever operate within a finite limited range one could assume therefore that everything made on this is therfore constrained to a small range no matter what you assign. Easy right?
    I honestly don't have a clue what you are talking about.
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    well lets assume verbal communication. The average human can only make a certain range of sounds with their voice. Also a human can only hear a certain range of sounds therefore your verbal language must be constructed from a subset of both. Now some sounds will be difficult for a human to make with their voice very high pitched sounds an opera singer can make for example will rarely be used as not many people can make them. whereas very low pitched sounds will be hard for people to hear thus less used. Now assume thatthe average human has a set lung capacity sentences will be limited in the range of the amount of air it takes to produce a particular sound and the sum of each sentence will not exceed a certain size without time for breath. This further reduces the range of possible verbal languages. aside from sounds difficult to string together tongue twisters and the like I dont see much else to affect possible verbal sounds to compose a language from perhaps you can suggest a few.
    Last edited by fiveworlds; May 7th, 2013 at 09:28 PM.
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    Brassica oleracea Strange's Avatar
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    OK. You are talking about the phonology of language. You are right; there is a finite set of sounds available for use in communication. Although this may be wider than you think. For example, there are a range of different clicks in some African languages and many other languages use sounds (whistles, gutturals, etc) that don't exist in English.

    The range of sounds (phonemes) used in languages varies enormously. For example, Hawaiian only has 8 consonants and 5 vowels, while English typically has 24 consonants and around 13 vowels. Neither of these are extreme. This may means that word are longer in Hawaiian, on average.

    But is more complicated than just the range of sounds, there are also rules about how they are combined. For example, many languages only allow syllables of the form consonant+vowel. English allows clusters of 2, 3 or more consonants together. Then there are factors like timing, stress, pitch ...

    All of this has little to do with the topic of the thread. As suggested in the OP, these sounds (and more importantly, groups of sounds making up syllables and morphemes) will have a statistical distribution, rather than all being equally common. This can, perhaps, be used to distinguish language from random utterances.
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    I would imagine you could could construct a probability density function out of these results.,Now there is a few ways of taking these results one way involves using a microphone and recording people as they talk. These recordings,are easily available and out of them one can see the waveform distribution of the particular sound or groups of sounds together mapped on a graph. here are examples http://www.google.com/search?q=audio...iw=320&bih=508
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  21. #20  
    Brassica oleracea Strange's Avatar
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    In principle, yes. However, it is not enough to just record a waveform. You need to do spectral analysis to identify consonants, vowels, etc.
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    You could also identify piano/guitar notes etc but I still dont see why that makes a particular set of sounds a language
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  23. #22  
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    Quote Originally Posted by fiveworlds View Post
    You could also identify piano/guitar notes etc but I still dont see why that makes a particular set of sounds a language
    If you were to analyse a series of sounds, you would find a difference between music, where there is a simple mathematical relation between the notes (as well as things like rhythm and progression over time), and "noise" where there is no necessary relationship.

    Similarly, the argument is, if you analyse speech sounds, you will see certain patterns (such as 'e' being the most common letter, or the fact that no words begin with 'bm' in English) which you would not see in a random collection of symbols or sounds. How hard is that to understand?
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    bmi,bma,bmp,bmw So what you need to do is isolate each of these patterns and attempt to find a correlation between every language on the planet
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  25. #24  
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    Quote Originally Posted by fiveworlds View Post
    bmi. So what you need to do is isolate each of these patterns and attempt to find a correlation between every language on the planet
    That would be a big job for every language. But you could certainly sample a number of languages (ideally from different language families) and see if they have consistent patterns. (Which I guess they will as they all use the same underlying brain mechanisms; because of this there are a number of universals in language beyond the range of sounds used.)

    But note that you would only have to look at English, say, if you wanted to demonstrate that patterns in English differ from random distribution. But if you look at multiple languages, you would probably be able to make a good stab at identifying languages by the distribution of sounds or symbols (even without understanding the words).
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    do you remember the idea of the babel fish from hitchhikers guide to the galaxy? I like the idea of a universal translator http://translate.google.ie/about/. But I also reckon that sometimes it isnt possible to translate a word in on langauge into another particularly if the word describes an animal there is no word for in another language
    Last edited by fiveworlds; May 8th, 2013 at 12:25 PM.
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    Quote Originally Posted by fiveworlds View Post
    do you remember the idea of the babel fish from hitchhikers guide to the galaxy? I like the idea of a universal translator Inside Google Translate ? Google Translate. But I also reckon that sometimes it isnt possible to translate a word in on langauge into another particularly if the word describes an animal there is no word for in another language
    I expect the Babel Fish will be an add-on for Google Glass.

    Of course it always possible to translate something from one language to another. It may require more or less words in each language, but that has nothing to do with the ability to translate it.
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    exactly. Do you think google glass will have a zoom option to make whatever the person is looking at appear closer?
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    In my opinion (if I may):
    Först of all, We must make clear if we're talking about a natural language (eg. chinese or latin) or a formal language.
    I assume you mean a natural language that could even be dead or extraterrestrial.
    In this case, statistics and frequency graphs would be helpful if you already know the language (or have some knowledge about it) but not otherwise, I'm afraid.
    Statistics can help you decipher an encrypted message if you know the language behind it but not otherwise.
    Picture yourself sitting att the end of a telegraphic line. You're getting a long row of morse signals (short/long).
    If you don't have a previous agreement with sender about the usage of those two signals, you will hardly be able to know
    if it is someone trying to communicate or a hen clicking with its neb/beak at random.
    That's my humble opinion.
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    which was a point of mine that some stretch of imagination goes into the meaning behind the sounds. However strange suggests that there is always a pattern to the sounds.
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  31. #30  
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    Yes, I think there will always be a difference between (natural) language and random noise. But I haven't found anything definite to confirm that yet. (I also suspect that a similar analysis of artificial language, such as a programming language, would be closer to random.)
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    I have just come across this: Language Log » From the American Association for the Advancement (?) of Science (?)

    I haven't read it fully yet, but it looks like the idea that language can be distinguished from non-language just by statistical/entropic analysis may be false after all...
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