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Bernd Einfeldt

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Somes questions, related to a more formal (mathematical) view on languages, I would like to discuss.

"In the beginning was the Word, and the Word was with God, and the Word was God." John 1:1

Nature does nothing without a purpose. Thus we may ask: What is the evolutionary reason for the development of a spoken language? I also would include mathematics and computer languages in these considerations and compare these to spoken languages. In this formal sense, we could even consider the information exchange that bees use as a language. Do all bees around the world use the same language? Does a sudden change of the location of the beehive affect the communication? Why do Asian and Western civilizations use the same mathematical language, although there spoken language is so different?
Is the mathematical language unique? I don't believe that there is a compelling reason that this must be so. Could a different mathematical language lead to a different view of our physical and economical world?

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  • Sep 25 2013: To Juliette Zahn and Mary M. a quote from Max Planck (below the translation):

    "Je reifer das Kind wird, je vollkommener sein Weltbild, um so weniger Anlass hat es sich zu wundern, und wenn das Kind erwachsen ist und das Weltbild eine feste Form angenommen hat, findet es diese Form selbstverständlich, und hört auf sich zu wundern. Aber nicht deshalb weil der Erwachsene die Rätsel der Welt gelöst hat, sondern nur deshalb weil er sich an die Gesetze seines Weltbildes gewöhnt hat. Warum aber gerade diese und keine anderen Geatzte bestehen, bleibt für Ihn ebenso wunderbar und unerklärlich, wie für das Kind."

    This is the translation using Google:

    "The more mature the child is, the more perfect his world view to it so less reason to wonder, and if the child is an adult and the worldview adopted a solid form, it is this form of course, and listens to wonder to himself. But not because the adult has solved the riddle of the world, but only because he has become accustomed to the laws of his world view. But why are these and any other laws, remains for him just as wonderful and inexplicable, as for the child."

    There are obviously some serious mistakes in this translation. My translation still not very good is

    "The more mature the child becomes, the more perfect his view of the world, the less it finds reasons to wonder, and if the child is an adult and the worldview adopted a solid form, it accepts this view of his world as self-evident, and stops to wonder. Not because the adult has solved the riddle of the world, but only because he has become accustomed to his worldview. But why are these and no other laws are valid, remains for him just as wonderful and inexplicable, as for the child."

    It seems that even with all the amazing advances in computing and even with all the smart people at Google, working to produce these helpful tools for us, a machine translation is still very rudimentary. I wonder why.
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      Sep 25 2013: Thank you for the wonderful quote......yes I quite agree, many times we stop our 'wondering'.
      However, I think that many of the members here on TED are quite the opposite. Some love the unknowns, and the wonderful discoveries we make on a daily basis as we listen to others and wonder around our world.
      There are many of us 'adults' who still have a child-like wonder........I consider myself one of them.
      I never, ever, get tired of learning new things, and making new discoveries.

      Now I will address your last paragraph...........you wonder why the machine translation is still very rudimentary? It is because it is not a human brain. That is my simple answer.

      I wish I could speak and understand Dutch.
      • Sep 26 2013: TED is a marvelous place for discussion. You are of course right, the translations is not correct because the machine translations cannot simulate a brain. A more fundamental question is: Is there a mathematical algorithm behind the human translation capabilities or are there principal mathematical boundaries. A group at MIT, working for google, is approaching this question. I think the work could give some insights into a common basis of languages. An old question, which already lead to (rather inhumane) experiments with children by emperor Friedrich the second and an egyptian pharaoh.

        PS: Planck wrote this in German, his son was sentenced to death by the Nazi Volksgerichtshof because of his participation in the failed attempt to assassinate Hitler.
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          Sep 27 2013: I have heard of many attempts at finding an algorithm for translation.
          Fascinating subject.....I know that translators make very good money.
          Once they find the algorithm, if one exists, then a lot of people will be out of a job.

          I am learning quite a bit about German history that I did not know before.
          Thank you for sharing.
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      Oct 13 2013: Dear Bernd,

      With my whole-hearted appreciation, I thank you for sending this wonderful quote. It intrigued a deeper understanding and three responses from me:

      1. My thought: the reason translation doesn't often work is perhaps because we need transliteration, which involves a great deal more than mere word conversion. (I think scholars from just about every corner of the world worked on translating from Cuneiform into modern English. How long did that take? And even then the message has yet to arrive at the common and collective understanding!!)
      2. My very daring ;-) expression of Planck's quote in English.(below A.)
      3. Something for you to enjoy in appreciation for your thoughtfulness.(below B)

      A. “The more a child grows towards adulthood, the more rigid his or her worldview becomes. Wondering (towards discovery and understanding) becomes less and less permitted. And by the time the child reaches adulthood, his or her worldview has adopted a fixed form. So if she or he does wonder, it is in this fixed and rigid form. Not because the adult has solved the puzzles of the world, but only because the adult has become accustomed to her own or his own worldview which was formed according to those rules. He or she accepts this view of his or her world as "self-evident", and stops to wonder. So the question of why these rules and not other rules have been etched in the adult, seems just as inexplicable to him or her as it does to the child. ”

      B. http://www.ted.com/talks/louie_schwartzberg_nature_beauty_gratitude.html

      Have a super wonderful day:)
      • Oct 13 2013: Yes, translations invokes a lot more than mere word conversion. The linguistic development in children is probably more related to a kind of logical decryption process, than to the process of learning a vocabulary.
        Thank for the link to the this great movie. Bees and other pollinator are part of this plant for over 100 million years. There current decline is really worrying.
  • Oct 16 2013: This conservation is closing tomorrow. Thank you for the comments and interest in my question, especially to Mary M. and Juliette Zahn.
    I think to understand the functions of the brain we must understand the mathematics related to learning and translating languages. John von Neumann differentiated between two different types of communications; those which do not involve arithmetical formalism, and those which do; i.e. communications of orders (logical ones) and communications of numbers (arithmetical ones). It is not self evident that these forms of communications are equivalent. Actually in Heisenberg’s matrix mechanics any attempt to offer a physical or intuitive picture of the process whose outcome could be calculated is given up, and requiring that the theory deals only with relations among quantities that could, at least in principle, be observed.
    But this implies that the logical communication cannot be translated one-to-one into arithmetical communication and vice versa.
    This indicates (if the laws of quantum mechanics apply to the brain physics) that a arithmetic language or a computer sublanguage which can be one-to-one mapped to a arithmetic language cannot be used to describe the brain. As Marry M. mentioned we probably have to develop a new mathematical language. Or maybe this mathematical language already exist, but we just can´t use on current computer systems.

    To Murray Gell-Mann: Since Bell´s theorem assumes that entangled particles have determinate values, it might be more related to a logical translation problem, rather than to the locality of physics.
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      Oct 17 2013: It has been a real privilege to have participated in this conversation.
      I wish you all the best Bernd.
  • Sep 29 2013: Thanks everyone for the interesting comments. I am on vacation for a few day´s. I currently I don´t like to access the internet through handy´s or unsafe public hot spots. I continue the discussion when I am back.

    PS: Mary M., I wish I had better communication abilities. I probably try it, when I am back from vacation, in my humble way. A quote from Carl Friedrich Gauss: "It may be true, that men (or woman - I think he is referring to both), who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation."
  • Sep 21 2013: Mary, of course sign language should be included in this discussion. It was just my narrow view on this subject which excluded sign languages. Thank you everyone for the comments. These help to see the subject in the right perspective. Albert Einstein gave in 1941 at the science conference in London a talk on "The Common Language of Science". I upload the english version for discussion to my blog http://discontinuous-flow.blogspot.de. In this radio address he say´s "....is established through the act of counting and measuring, who´s performance is sufficiently well determined". The english translation is actually incomplete. In the German version Albert Einstein added the words "at least within certain boundaries". I think this is important. Are there boundaries for the description of nature through a (mathematical) language? Do we need a new kind of mathematics to understand the universe in the infinitesimal small?

    PS: There is a problem uploading the audio. However it is on YouTube http://www.youtube.com/watch?v=td2SReWxogY
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      Sep 21 2013: Thank you Bernd for your reply.
      I sure wish I could answer your questions about needing a new kind of mathematics to understand the universe in the infinitesimal........I hope someone with a more scientific background contributes to your wonderful conversation.
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      Sep 22 2013: Thanks for the youtube video addition, I just watched it.

      If I am understanding Einstein correctly, he was trying to show how the language of science has brought people from all over to work cooperatively for the betterment of mankind. And that in the future, all positive outcomes will depend on the goals scientists worldwide embrace.

      There were a few things he said which I don't know if I agree with. Especially since I am reading the book about a deaf child, and I'm learning how cognitive skills developed in her, despite the fact she did not have language.

      I may be wrong here Bernd, but from my perception, I thought he was trying to make mathematical language (he mentions Geometry and Algebra) superior to other languages......because of how it is the same no matter where you apply it....in whatever nation, independent of the culture's language.

      This discussion is a very good one for a linguist and mathematician to join.

      I am but a humble teacher of small children.....I'm afraid my language is limited to discuss the lofty ideas Einstein brings out.

      I hope others join this conversation...it is very interesting.

      I don't know how long you have been participating on TED, but usually when you reply to those who contribute to your conversation, great things happen.
      There are people reading through these conversations, without contributing......unless they read something that catches their eye, or they know the answer or have a reaction to someone's statement.
      Why don't you try and reply to those that have commented so far? Maybe you'll get further along in your quest for answers. What have you got to lose?
      • Sep 24 2013: Is human communication governed by more then one component? This might be related to the humans incredible ability to throw an object very precisely on a target; related to the so called throwing hypothesis - I am not an expert in evolutionary biology. Maybe someone more knowledgeable in this field is interested to join the discussion. The book by William H. Calvin about the "Throwing Hypothesis" could be a good source for more scientific information. There is also an article in the science magazine on "Numerical Cognition Without Words: Evidence from Amazonia", (http://www.sciencemag.org/content/306/5695/496.full) which I think is very reasonable. There are many really smart kids with dyslexia and vice versa - some people have the ability to give wonderful speeches without any logical content. In the science article the question is posed: Are there terms that exist in one language that cannot be translated into another? Well, there are certainly terms in the mathematical symbol language which cannot be translated into a spoken language and vice versa. It should not be difficult to give some examples.
        The other part of languages is probably much more fundamental. Using the words of Remo H. Largo: "The language has one of its most fundamental roots in the relationship behavior of humans". He described in his book "Baby Years" ("Babyjahre") very nicely observations related to the language development in infants.

        Einstein´s focus is obviously on the logical part of languages and I think yours on the relationship behavior part. Both are important parts for our society,
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    Sep 19 2013: Do not miss this rare gem!!

    23,000 km (14,291miles) closer !! at 362,264 Km!! (225,100 miles)...spectacular math....(for which, professor Dr. Gell-Mann would surely grant a computer break :)) outside your window right now. I hope you enjoy tonight’s lunar perigee, as it’ll be "the moon’s closest pass to Earth until December 4, 2013"
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      Sep 21 2013: Here is a small poem I used to have my second graders memorize when we studied the moon and the solar system: Enjoy!!


      Are you lonely, Moon?
      You giant white balloon!
      You have no water, wind or air.
      No wonder, nothing lives up their.
      You can't grow trees or flowers or grass.
      Your soil is only rocks and glass.
      Even your light is not your own.
      Instead it's from the sun that's shone.
      Your gravity is weak, I hear.
      You really have no atmosphere.
      But don't be sad, Moon, please don't cry.
      For I still love you in the sky.

      Meish Goldish
      • Sep 24 2013: Like this poem, it teaches children that there are different worlds and maybe a child ask are there other places like earth or other moons?
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        Sep 24 2013: Lovely poem Mary Thank you :-)
        Did you know that there are 180 moons in the solar system and our planet is the only one known to have intelligent life!! I didn't!! Did you know that our one and only moon is the reason why we were able to live and evolve on Earth because it not only regulates the ebb and tide but it stabilizes the rotation of our home planet making it habitable all over!! Thats a lot of loving work!!

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          Sep 25 2013: Glad you liked the poem.
          I actually did know the facts you mentioned. They are in a booklet I have on life and all it's beauty.

          The booklet calls the Moon, the "perfect neighbor". And it goes on to say...."If you had to choose a "next-door neighbor" for the earth, you could not improve on the moon. Its diameter measures just over a quarter of that of the earth. Thus, when compared with other moons in our solar system, our moon is unusually large in relation to its host planet.

          The moon is the principal cause of ocean tides, which play a vital role in earth's ecology. The moon also contributes to the planet's stable spin axis. Without its tailor-made moon, our planet would wobble like a spinning top, perhaps even tipping right over and turning on its side, as it were. The resulting climatic, tidal, and other changes would be catastrophic."

          I learned, a long time ago, that we live at a very special address in our solar system.
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          Sep 27 2013: Welcome.
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    Oct 4 2013: I have been reading a bit about languages.......look at these points:

    "Different languages require different thought patterns, making it difficult for a new learner to ‘think in the language.’ This is also why a literal translation of something said or written in an unfamiliar language may seem illogical, often causing persons to say, in effect, “But that doesn’t make sense!”


    "We find, for example, that certain languages are monosyllabic; that is, made up of words of only one syllable. Chinese is an example. By contrast, the vocabularies of a number of other languages are formed largely by agglutination; that is, by joining words placed side by side. For example, the German word Hausfriedensbruch literally means “house peace breakage.” More understandably to the English-speaking mind, it means “trespass.” In some languages syntax, the order of the words in the sentence, is very important; in others it matters little. So, too, some languages have many conjugations (or verbal forms). Others, such as Chinese, have none. Countless differences could be cited, each requiring an adjustment in mental patterns, often with great effort."

    So, do you think that all languages stemmed from one language?
    I'm curious for your thoughts.
    • Oct 12 2013: It is obvious that if we could find characters or signs suited for expressing all our thoughts as clearly and as exactly as arithmetic expresses numbers or geometry expresses lines, we could do in all matters insofar as they are subject to reasoning all that we can do in arithmetic and geometry. For all investigations which depend on reasoning would be carried out by transposing these characters and by a species of calculus."

      Gottfried Wilhelm Leibniz (*https://en.wikipedia.org/wiki/Leibniz)

      Remo H. Largo wrote (translated): "The analysis and the forming of speech sounds is for all humans the same, independent of the native language…….the biological foundations are the same for all languages. Thus it is understandable that small children everywhere on this planet form, in there first month, the same sounds.

      The mental development precedes the linguistic development. First a children develops an intrinsic understanding, then it understands the linguistic notion which denotes the concept, and finally it learns to use the linguistic notion."

      I think it is reasonable to assume that there is common fundament for logical human thought pattern.
    • Oct 12 2013: Mathematical symbolic logic is probably an approximation to such a language, which makes the calculations feasible which Leibniz mentioned. "Leibniz's idea of reasoning through a universal language of symbols and calculations foreshadows great 20th century developments in formal systems."
      In a post (http://discontinuous-flow.blogspot.com/2012/09/turing-machines-and-mathematical.html) I asked the simple question: Can our modern formal symbol system (on which natural sciences is based) exists in a real physical finite object (human brain, computer). The answer is that such an physical object cannot exist in a real finite volume. Thus there must be some transcendental aspects in our logical foundations.
      I then asked the question if we can find a formal symbol system, which can be used to describe physical objects and which can exists in a real physical object? I believe the answer is partially positive. But this question requires a focus on this subject, impossible if the daily occupations are of a totally different nature.
  • Sep 28 2013: Maybe I should start my own business and develop a new translation algorithm with puts google out of the translation business. Just joking - there is no chance to compete with google, not because it is not possible to develop a better translation algorithm, but because I cannot compete with there research, management and marketing resources. Anyhow, if someone is interested to risk some money, please drop me line. I would be great if I could apply my mathematical knowledge and talent, (after over twenty years working as a consultant to make a living) finally to something which I think is more useful for the society. I would rather use a word wave representation and not a word vector representation, as the Google team did it - it should not be a surprise if this would reveal a quantum mechanical description of languages.
    But in Germany it is probably easier to get funding for a new kind of cereal mix.

    Yes Mary M., of course, progress has always also a downside, the invention of typography put at lot handwriting translator out of business, the translation of the Bible by Martin Luther the reformer put the catholic church out of the indulgences business and today the internet gives public access to a world wide knowledge base, which will put parts of the established information distribution industries out of business - but this is another discussion.
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      Sep 29 2013: Well, with the internet, you have a lot of options.
      Perhaps contacting some of the TED speakers directly, with your ideas, and who knows?
      Maybe you will have success.
      Never say never Bernd.............."easier to get funding for a new kind of cereal mix"? huh.....too bad.
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    Sep 19 2013: I am currently reading the book Deaf Like Me.
    It is the story, told from the fathers view, of having a deaf child.

    I am seven chapters into the story, and already I am starting to appreciate the important role language plays in our lives.

    The desire to communicate is very strong......I found it peculiar that you left out sign language from your OP

    And may I ask, what do you mean by 'mathematical view of language'........are you referring to patterns that might eventually show that all languages originated from on single language?

    And have you seen today's TED talk about patterns?
    I think you might enjoy it very much.
  • Sep 19 2013: "What is the evolutionary reason for the development of a spoken language?" Perhaps because two or more animals can do things that one cannot if they are all sharing the same thought. With more animals, the need for a more complex form of communication exists.

    "Is the mathematical language unique?" I do not think so. It is just and evolved shorthand used by people interested in communication with other humans about particular set of problems or observations.

    "Could a different mathematical language lead to a different view of our physical and economical world?" TBD. You might argue binary and computer languages have recently achieved this by enabling us to interpret massive amounts of data by breaking things down to a very simple level and being able to do simple things very fast.

    Perhaps in a future generation, there will be a method for directing a researcher to the most likely technologies to help solve a new problem, thus enabling him to narrow the field very quickly and be led to intuitive leaps necessary for subsequent technology breakthroughs.

    Sort of leads us to the importance of education... :)
    • Sep 24 2013: Thanks for your comment Robert. Like your last sentence "Sort of leads us to the importance of education... :)". Unfortunately education is streamlined in Germany and I doubt that we today really know what is important tomorrow. I am not so optimistic concerning that there will be a method for directing a researcher to the most likely technologies to help solve a new problem, thus enabling him to narrow the field very quickly and be led to intuitive leaps necessary for subsequent technology breakthroughs. After decades we still don´t have computer which can make a good reasonable translation and computer did not help us really to avoid the financial crisis.

      Please see also the Lejan comment.
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    Sep 18 2013: 'Do all bees around the world use the same language?'

    What a beautiful question and to sad I don't know the answer to it. So lets do some educated guessing here... :o)

    Even though the ability of communication is embedded within the DNA of species, its does not seem to also have a specific 'character set' or 'word-list' embedded into them, but the given restrictions and 'tools' for communication itself.

    By this and evolution I would not be surprised if bees would have developed a variety of dialects across different sub-types and of different locations of the same type.

    Slight variations in temperature signatures, biochemical transmitters as well as repetition of certain movements could have developed different meanings or changes in the information content, yet on this, experts probably know better.

    'Does a sudden change of the location of the beehive affect the communication?'

    It certainly does, as worker bees communicate vividly about the location of food sources in relation to the current hive position and once this position gets changed, the communication has to adopt to it and thereby gets effected.

    This rises another interesting question: Is there a critical distance at which a returning bee would not be able to find its way back to its re-positioned hive? And if yes, which distance is it?

    'Could a different mathematical language lead to a different view of our physical and economical world?'

    Definitely! As the beginning of our common mathematical language is based on the numbers of our fingers, it also categorized our 'felt value' system within this decimal system, which becomes clear if you choose to work within others.

    Nevertheless it seems, that our mathematical system does resonate with the mechanics of our world, yet so may others as well, as those would only be transpositions of what seems to be valid operations and logic.
    • Sep 24 2013: Thanks for you comment Lejan, are you currently working in Aachen; Germany? The Pirahã study mentioned in my last reply to Mary´s comment, posses the question: Is the development of a mathematical (arithmetic) language a cultural achievement, related to the needs of a more complex society? If this is true it posses some further questions. Questions about the uniqueness of the mathematical language and even more important; can this cultural achievement be partailly lost? Comparing old mathematical books and some more recent mathematical lecture books, one could get the impression, that this has happened in Germany. The question also arises if the mathematical and the spoken language can be modeled through a single digital computer system? Can a computer system ever become more human if it is based on a digital language?
      Actually John von Neumann noted in his book "The computer and the Brain" that the nervous system is based on two types of communication: those which do not involve artithmetical formalism, and those which do, i.e logical communication and arithmetical communication (communication of numbers); see @berndaushamburg for this page in the book of John von Neumann book.
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        Sep 24 2013: I have been a student in Aachen till the mid 90s yet never returned to work there.

        For the development of a mathematical language I would think, that a 'more complex society' is a basic necessity for this to happen and less determined by the needs of such.

        In early societies in which a distinct 'division of labor' hasn't developed, there might have been not enough 'leisure time' to ponder about mathematical matters, as the people have been to busy in securing their daily food supply. Harsh environmental conditions such as cold climates and limitations in arable land would have kept those societies busy enough not to expand their mathematical languages beyond their very basic practical needs.

        On this I think it is no coincidence, that the cradles and 'high times' of mathematical and also philosophical development is mainly located within 'warmer' regions of this planet which also happen to be naturally fertile to agriculture. As those conditions tend to speed up the division of labor, which then in return enabled talented thinkers to have the time needed to do their thinking.

        From there, specific 'needs' of this more complex societies for mathematical solutions did of course influence the order in which the progress was made in this field, yet it seems there was still enough time to ponder about mathematics in general.

        I never came to confirm this, but I once read an interesting explanation why so many Indian people tend to be very good in understanding mathematics, compared to other nations. The reason was said to be related to high similarities in abstraction levels in the spoken and the mathematical language. If this is true and covers the whole variety of spoken languages within India, I don't know, yet if it was, at least for certain dialects, it would make much sense to me.

        As for schoolbooks, Germany is the best example how get those screwed up beyond recognition And It was just laughable if its consequences weren't that serious.
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        Sep 24 2013: German schoolbooks aren't designed to help understanding a certain topic, they are designed to maintain a false academic claim on complexity and stick to the following guidelines:

        1) Nothing is simple. And in case something is, make it appear not to be.
        2) Use as many foreign words as possible. It sounds smarter and helps 1) to work.
        3) Do not visualize. And if it can't be avoided, use pictures only a view are likely to follow.
        4) Never draw on similarities, as those might give students insights.
        5) Repetition in learning is overestimated and not to be supported.
        6) Paper is expensive. Reduce example exercises and don't give them step by step.
        7) Introduce abstract variables asap and BEFORE a concept is understood.
        8) Insist on the very way a problem has to get solved, not to get it solved.
        9) By all means, never introduce any 'sense of proportion' in average students.

        I remember vividly how angry I was, and still am, when I once got hold on a lecture book about thermodynamics from a US University, which introduced this topic in a way, that was easy to follow and highly understandable. Not long before I struggled through the same topic at a German University and barely made it through the examination. And this more by chance than true knowledge. Since then I know it wasn't me who didn't just get it, but that Germany has a fundamental problem in designing good school books and lecture books aiming at realistic and 'average' intelligent students.

        Recent Pisa studies may proof, that ‘this cultural achievement' is in decline, of which our German school books got a lot to do with.

        'Can a computer system ever become more human if it is based on a digital language?'

        No, as it can only become more 'human like' and seems to evolve beyond its digital language it was originally written in. Programmed neural networks are not understandable anymore to their programmers and exceed the borders of its original programming language.
        • Sep 26 2013: Well, I am not knowledgeable enough to comment on your points above; interesting - any references?

          I think teachers in schools in Germany make an impressive good job and I think my children are lucky to have very good teacher. On the other hand, teachers in Germany are tied to rather rigid formal specifications and there is only little freedom to make teaching individual. The children they have to teach are obviously not all the same, in all classes and all regions. I don´t know if the "fit´s all children in a class" approach is what we really need for a complex future. Children are so wonderful different and every child can contribute to our society in a different way.

          When I was looking some time ago for a book from Arnold Sommerfeld about partial differential equations, I could only find the english translation?
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        Sep 26 2013: I smiled too while summarizing the essence of German 'schoolbook design' and there are certainly exceptions to find, yet as for a reference, what do you find in your children's schoolbook concerning the German language for the term 'noun'?

        Do you find the term 'Substantiv' used in the book or the term 'Tätigkeitswort' instead, which has not only the same meaning but also originates from the German language. And there is even another advantage to it, as the term 'Tätigkeitswort' is self-explanatory to a German speaker as it combines the term 'Tätigkeit' (to do something) with the term 'wort' (word) of what is what the nature of nouns is about.

        'Substantiv' instead originates from the Latin language and is by its nature not 'self-explanatory' to a native German. It may still be to Italians, I don't know, yet not to us. Especially if you are a young German student and none of your parents Italian... :o)

        The generation of my parents, which was born during WW2, learned the German grammar using the term 'Tätigkeitswort', whereas to my generation, borne in the late 60s, the term 'Substantiv' got introduced, which as to my knowledge is still in use today.

        And even though I am no teacher by profession, I dare to claim that for learning purposes things ought to be kept as simple as possible and as helpful as possible so that anyone gets to understand them. And if this was true - of what I think it is - then it should be obvious to choose any 'self-explanatory' term over any other less useful alternative.

        And as I also dare to claim, that 'consistency in terms' is essential to learning, as it avoids confusion, there is actually no logical reason why self-explanatory terms should ever be substituted in schoolbooks.

        And no, I am no 'hardcore' linguist who fights his 'mother tongue' off any foreign influences. On the contrary, I think our language gets enriched by them and evolves as dynamic as any other. But here we talk about learning, where it does make a difference.
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        Sep 27 2013: There was a time in which scholars used Greek and Latin not only because most of the available literature was written in those languages, but also to 'cover' their knowledge towards this uneducated mob of farmers and workers of those days.

        Martin Luther wasn't seen as 'persona non grata' by the Catholic Church for no reason...

        And science, which evolved out of alchemy in those days, was no better than the Vatican.

        You may have heard about the recent studies in which Germany ranked lowest within Europe regarding 'social classes' and 'equal opportunity' towards education. By this it is more likely for children in Germany from low income families not to archive an University degree than for children of high income families. Even though it is almost free of charge to attend a University here and that students from low income families get special financial support by our government.

        So the reason for this 'inequality of opportunity' in education in Germany seems to be inbuilt in the educational system itself. And I personally think, it is.

        You think that ' ... teachers in schools in Germany make an impressive good job ...', and without doubt, I think so too. And the point-list I made didn't aim at those teachers, it aimed at German schoolbook design, of which I am sometimes in strong doubts that German teachers are even allowed to have their say in. :o)

        And although we certainly have many capable teachers, all of them are victims of and stuck in the given education-system themselves. Many friends of mine are teachers for different schools and what I get to hear by them is frightening me at times. The system isn't coming to rest, as any new and negative Pisa study result keeps changing anything over and over again, yet does not identify its true problems. There is to little financial resources in the system, many schools don't have enough teacher to establish a solid framework of operations. The system(s) drown(s) in regulations with no equal national standards ...
        • Sep 28 2013: Where would we stand today without a Reformation and the translation of the Bible by Martin Luther from Latin into German? Would we still live in a clerical guided society which fights other religions? Would we consider the black death, climate change, tsunamis or a comet impacts still as given? My historical knowledge is only rudimentary, but I think the outrages of famers in the middle ages are mainly related to the burdens they had to carry.

          Martin Luther said these words at the imperial diet

          "Unless I am convinced by proofs from Scriptures
          or by plain and clear reasons and arguments
          I can and will not retract
          for it is neither safe nor wise to do anything against conscience.
          Here it stand. God help me. Armen. "

          assuming that he was finished after saying these words. He was declared an outlaw, may be killed by anyone without threat of punishment.

          Replace "Scriptures" by "a Constitution" or "Science" and you get some sentences with remarkable relevance.
  • Sep 18 2013: For a start, nature does nothing with purpose, not the other way around.
    The evolutionary process has no goal in mind, after all.

    From a purely evolutionary standpoint however, language has tremendous benefit. Even for a hunter gatherer, being able to organize people towards a single purpose allows for things that we would not be able to accomplish as individuals. Whether hunting, building, fighting or farming, language is necessary to coordinate.
    Seeing as a coordinated group is capable of much more than an uncoordinated one (especially in a fight), the benefits are obvious.

    Mathematics and computation also have tremendous benefit, though by the time they rolled by, the evolutionary process in humans was already halted by such a thing we call civilization. Ruthless statistical culling out of the weak and unfit is the very life's blood of evolution, but doesn't sit well with civilized life.
    Evolution is still occurring to some extent, but its a very different beast than what it used to be in the state of nature (which is rather horrible to live in, by the way).
    • Sep 24 2013: Thank for your comment Nadav, Mathematics and computation also have tremendous benefit. I wonder if there are some studies which link these benefits to a monetary scale .
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    Sep 18 2013: You may find interesting this article on the origins of mathematical symbols: http://www.encyclopediaofmath.org/index.php/Mathematical_symbols

    Note the differences in representation of the standard polynomial, for example.
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    Sep 18 2013: "Nature does nothing without a purpose. "

    it is already false. our current knowledge is that nature does nothing with purpose.
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      Sep 18 2013: Did you have a purpose in providing such an answer?
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        Sep 18 2013: can't answer that in any scientific model
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          Sep 18 2013: figures....
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          Sep 18 2013: I may be missing something here, but I thought your purpose was to question the premise. Questioning a premise is typically quite legitimate as a response to an argument.
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        Sep 18 2013: Yes, he had. Interestingly he does not seem to welcome the same purpose to be applied to his own comments and those who do are then just 'goofing around' ... lol :o)
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          Sep 18 2013: I like to goof around with Krisztian.......he's always so serious.......especially when he hasn't had his chocolate fix-for-the-day. ;o
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        Sep 18 2013: LOL!

        Oh Mary, you just woke my cat by making me laugh out loud ... ;o)

        But yes, TED conversations would be less interesting if Krisztián would have had his share of chocolate... :o) Actually, he is pretty clever in his very way, which makes in even more interesting to goof around with ... :o)

        It seems Austrian economics generates humor only in those who doesn't believe in it ... ;o)
        (Sorry Krisztián, I couldn't hold this one ... ;o))
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          Sep 19 2013: Sorry about your cat Lejan (not) ;) I hope he/she didn't scratch you....Meow....

          Yes, I also enjoy his cleverness.......

          Humor is very important, imho.
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        Sep 19 2013: Nope, no scratching, just the usual look of disgrace of the sort I usually get and AFTER I opened the food can for her ...

        On humor I agree with you!
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          Sep 19 2013: LOL!!

          Well, cats definitely have a purpose in life......to keep us humble.
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        Sep 19 2013: :o)

        For the sake of todays remaining harmony, I will withhold this wisdom from my cat until she starts to like me again... temporarily, for my opposing thumb ... ;o)
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          Sep 27 2013: Thanks for the youtube link to the moon documentary.
          And a female scientist narrates it!!
          That's just icing on the cake Lejan!!!
          I'll enjoy watching it tonight.
          Thanks again!!!
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        Sep 27 2013: And she is a very good narrator too!
        And a good scientist, as I assume she did a lot of the consulting side as well.

        All the rest goes to good old BBC's craftsmanship for excellent documentaries.

        You are welcome, enjoy the cake and let us know if you learned something and if yes, what its was ... and if no, how you come to know all these things ... :o) lol
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          Sep 27 2013: That video was absolutely stunning!
          I loved that she showed us all the wonderful things that happen due to the moon......I've fallen in love with the moon all over again!!

          And, despite what you might think, I am NOT a know-it-all.............LOL ;)
          I did learn ONE knew thing..hahahahaha

          The BBC documentaries are always so wonderful.
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          Sep 27 2013: Thank you. Excellent documentary!!
          I learned lots.....ex: that the moon is moving away from the Earth....and that our finger nails grow at the same rate as the moon is moving away from the Earth!!.....that makes me wish I could slow the growth of my finger nails to make the moon stay where it is:-)
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          Sep 27 2013: I had no idea that there was a BBC Scotland....is that where the documentary originated from? I did not catch that detail, I always assumed it was London.

          How do I picture the moon....masculine of feminine........huh.....I guess I have always pictured it neutral.........perhaps from being bilingual, I say la luna in Spanish and the moon in English.......so my mind gave it no particular orientation......it is just an object.

          What a peculiar question. How original of you!

          Have you ever seen the rapids that are in the beginning of the video?
          That must be really exciting to navigate in.......I was sitting on the edge of my seat feeling a bit anxious just watching her in that boat.

          I, like Juliette, also thought it interesting that the moon is moving away from Earth......couldn't it be possible that instead of moving away, it is just following some sort of orbit, and eventually it will come back around to being closer?
          I mean, I'm no astronomer, but isn't that possible? What do you think?
        • Sep 28 2013: Like the BBC documentaries, hope this series continues for many years and that they can retain the quality in times of tight budgets. One of my favorites is "Das Wunder des Lichts", don´t know the english title.
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        Sep 27 2013: You probably learned, that there is such a thing as BBC Scotland, which, not to long ago, was absolutely new to me ... ;o)

        Yet I am glad you liked it.

        If you think about the moon, how do you picture it? Is it 'masculine', 'feminine' or 'neutral' to you?

        In the German language the moon is masculine, which is indicated by the masculine article 'der' in 'der Mond'. Whereas Earth is feminine and called 'die Erde'.

        What I found interesting was, that as I take a step south of my country, in Italy both are seen feminine, 'la luna' and 'la terra', and one step to the west, it is the same with the French 'la lune' and 'la terre'.

        If I remember correctly, you are of Spanish origin, which would give you the moon as a 'she' as well, yet did the English language influenced what the moon is to you today?
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        Sep 27 2013: Yes, there is a BBC Scotland and it operates even independent from BBC London. They also have a radio program which is in broadcasted in the Gaelic language.

        Thank you for your answer on how you picture the moon and it is interesting to see how different one and the same 'object' as you named it gets perceived.

        In many respects my story is similar to Maggie Aderin-Pocock, the narrator, regarding the moon. As a child, the moon fascinated me and so we became friends and companions ever since. Like Maggie I was dyslexic as a child and got hooked on science to graduate many years later in aerospace technology in the same hope to get somewhat closer to what fascinated me. And as it worked out for Maggie, it didn't worked out for me, as for other reasons I choose a different business later on. Nevertheless, the moon has never been just an object to me and is deeply rooted in my spirituality, which is pagan by its nature.

        As for the orbit of the moon, it would need a force for it to come closer again, which isn't there.

        The extra force the moon gets to spiral out of us, is the equivalent of the braking effect it has on earth and which gets exchanged via gravity. Just to stay where it is, the moon needed an equally strong force of this 'breaking energy' pushing on its far side, of which there is none.

        Also there is no 'memory buffer' or 'force buffer' in orbit mechanics which would release certain fractions of force over time which it might once received by some other impact. So besides some 'damping' and time relaying effects due to inertia, for the moon there is nothing to expect by now for it ever to return towards us again.

        So our only hope now is Juliette Zahn and if she manages to gain control over her fingernails ... :o)

        Mind over matter over time ... go Juliette, go, go, go ... ;o)
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          Sep 28 2013: I am going to come back and reply to this later on......I have a busy day.......
          Lots of information to digest here.
          Catch you later!
          Say hi to your cat. :)
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          Sep 28 2013: Huh, so, there is no chance that the moon is just moving in an orbit farther away, and then will come closer? You are sure that there would be a force needed to bring the moon back.......well then, I'm glad she said we are in no immediate danger, since it would take millions of years for the moon to ever get far enough away to create any harm to earth's environment.

          As I thought about this movie, and reflected on the beauty of our planet, a thought struck me. We are in constant motion......revolving and orbiting the sun. And our galaxy is also moving through the universe. Yet, our atmosphere, is always around us, protecting us. We have a wonderful shield that protects us from solar radiation. I do not think the majority of humans truly know how wonderful our earth environment is.

          Something else that I found rather interesting from the video was how the distance between our earth and the sun and the moon, allows for those beautiful full eclipses. And even though the moon and sun are not the same size.....the distances involved allows for that phenomenal event every so often...Monday August 21, 2017 is the next one. The last one we got to see from the US was back in 1991.

          And yowza.....did you see Mars bouncing all over?......I wish I had known that when I taught the lesson on the planets. My second graders would have loved it.

          So, how exactly does the moon fall into your spirituality? Do you have any rituals or traditions, or is it more of a meditative, kind of spirituality. I hope you don't mind me asking.
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          Oct 4 2013: "Remember the moon stays bright, when it doesn't avoid the night.":-)

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        Sep 28 2013: The English title of this BBC documentary is called: 'Light Fantastic'
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        Sep 28 2013: No stress please, my cat sleeps anyway ... ;o)
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        Sep 28 2013: Yup, I am positive that a force is needed to push the moon back to us. Take my cat for example, to which I couldn't pass your 'hi' over, because she is sleeping almost the whole day now. She lays on my bed and doesn't move anywhere in relation to me. So if I wished her to change position, I had no other alternative but to apply a 'force' on her for this- and despite all consequences - to happen. No force, no moving cat ... its that simple ... :o)

        'I do not think the majority of humans truly know how wonderful our earth environment is. '

        And this is exactly the reason, why we keep poking holes in this our life-jacket while floating in this all deadly ocean.

        In fact, earth is making its way through space pretty quickly. And even my cat, which is still not moving relative to me, is orbiting around the sun at a speed of about 66.616 mph. 'On top' of that, she also orbits around the center of our galaxy at about 503.310 mph. And even though she appears to me quite lazy today, she has overcome a huge distance since she balled up this morning... :o)

        So next time the officer hands out your speeding ticket, you can be grateful for the point of reference he/she choose to measure your speed ... :o)

        I think it is amazing that we live in times, in which by chance we have this beautiful event of the total eclipse. Unfortunately, I missed the last one in Europe, as I have moved to your country just a view days before. Yet there are others to come to have a look at, hopefully ...

        How did you experience the interest of your second graders on that topic? How did they perceive this knowledge? Have the been highly into it, or did they remain on 'average' levels?

        My spiritual connection to the moon is difficult to explain, but I do not follow any tradition nor have I any rituals surrounding it. It is more of an high respect and awe about this ancient cycle. Whenever I am not aware about the current phase its in, i know I have to 'slow down' and to readjust my perception of time.
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          Sep 29 2013: I have a quote in my collection that reads:

          "Living on Earth is expensive, but it does include a free trip around the sun every year".

          Your reflections reminded me of it.

          I find that small children are naturally drawn to astronomy. They are fascinated with outer space. The unit I teach on the planets includes details of the entire solar system.
          I spend an entire month on it. One of my favorite activities is to observe and draw the moon during it's Lunar cycle.
          The vocabulary...........New moon, crescent moon, gibbous moon really gets the kids very excited ......little 7 year olds love to talk "science"............they feel like experts when they own the vocabulary. You should hear them talk and argue over the kind of moon that was out the previous night. They are too funny.

          Look at one of the activities we do to see if the kids understood the lesson (We use Oreo cookies)


          I remember seeing a set of prints at Restoration Hardware (a local store) that were really nice too.....look....


          I guess I understand how you feel about the moon.
          I kind of feel that way about the constellations visible during the cool winter nights.
          I crane my neck back and walk indoors staring at the sky.
          The universe, in it's entirety, is very awe-inspiring.

          Wouldn't it have been something to be alive 3,000 years ago when we could have seen the milky way easily?

          A place I would love to visit is Chile.......where the European Southern Observatory has it's telescopes. Have you seen this time lapse video done by them?


          Did you ever see this talk?


          That is where I first learned about the observatory in Chile.
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        Sep 30 2013: Thank you for all this interesting information.

        I am very glad to hear that small children are still drawn naturally to astronomy, and this despite their highly distracting environments of today. Yet if I would have been in your class. I would have not learned about the lunar cycle, as all of my cookie models would have disappeared mysteriously from my desk ... probably by the presence of a nearby black hole ... :o)

        The milky way still isl easily visible today, just stay away of lit areas, such as cities or villages and this on clear, dry nights and best in wintertimes. Once you are out of this backscattering 'light pollution', you will get to see the whole beauty of our galaxy. Chile is fine, but no necessity to get a fine view on our stars with our eyes.

        I haven't seen the video you linked and will have a look at it soon. Thank you.
  • Sep 18 2013: There have always been such feelings from worlf to Sausaure to N.. m Chomsky. Okay i can't speel these names.
    • Sep 18 2013: Well - mathematics is not about feelings, it is about structures. If you understand the structure it does not matter how you spell a word.
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        Sep 19 2013: "If you understand the structure it does not matter how you spell a word."

        That is very true.
        As a matter of fact, we had a whole conversation on this very topic:

      • Sep 19 2013: I didn't understand why Noam Chomsky abandoned generative grammer except it was a model that was overly complex. Basically I wonder if you issues involve modeling? There is so much about that now. Digest it a bit and respond. I keep thinking about building a model.