Thank you for your comments.

You wrote that:

"Popper remarked that in the growing of knowledge the problem is not precisely how we describe the world, in spite of our inability or incapacity to express our ideas by means of theories, but to develop new approaches and insights that help us understand nature no matter the language."

However, it is the language that shapes our way to think and, hence, to develop new approaches and insights. A proper care of the language is important in understanding the most fruitful ways to study. Otherwise, you can lose your time on false problems, because the words drive you in the wrong way.

Good luck for your essay.

Luigi

Thank you very much for having pointed to me your interesting essay. I am always happy to read that other people thinks about the importance of the language. I did not know the essay by Fortun and Bernstein: it seems to be interesting and I have ordered it to my bookshop.

Thanks again for your note.

Luigi

Thank you very much for having pointed to me your interesting essay. I am always happy to read that other people thinks about the importance of the language. I did not know the essay by Fortun and Bernstein: it seems to be interesting and I have ordered it to my bookshop.

Thanks again for your note.

Luigi

Dear Luigi,

I enjoyed reading your interesting essay. Your perspective on the importance of the role of language in the first half of the paper is something also discussed in my essay. It seems we make several of the same points in slightly different ways.

Regards,

Tom

    Recently the Navier-Stokes equation has an equivalency with the Einstein field equation.

    http://arxiv.org/abs/1101.2451

    The solution sets of the two can be mapped into each other. This is an interesting development, for this is a functorial map between different linguistic sets.

    Your paper is good.

    Cheers LC

      Thank you for having pointed to me this work. I'll read it.

      Cheers,

      LF

      Dear Tom,

      I've read and appreciated your essay. It is really interesting and I am happy to see that you too pointed to some concepts common to my essay.

      I have a couple of notes. First, you cited and agreed with Heisenberg, when he wrote that Galilei shared Plato's ideas. No, Galilei was not a platonist, as underlined by his linguistic concept of mathematics. Mathematics as a language is at odds with the platonism, where ideas are something a priori with respect to human beings and the language. Indeed, Plato spoke about maieutics, which was a concept of knowledge based on reminding something already existent and known. This is really not the concept of science emerging from the text of Galilei.

      I think that one important step missing in Heisenberg's essays and yours is the Renaissance, which was mandatory to prepare the right cultural humus where Galilei's science could grew.

      Another point refers to the fact that you made examples of measurements of finite quantities and you conclude that the nature could be described only by discrete languages. Obviously, if you consider only finite quantities, you will obtain a digital answer.

      In addition, by writing that, you implicitly say that there is no infinite in nature, while there are examples pointing to its existence, such as the curvature of a spacetime singularity.

      Good luck for your essay in the contest!

      Cheers,

      LF

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      • Post #17

      Dear Luigi,

      You have written a nice essay, much of which I am in agreement. However, I believe that you have made a mistake in the definition of your premise. You wrote:

      "The two pillars of any language are syntax and semantics. The former deals with the basic formal structure of the language, while the latter refers to the meaning of the signs and symbols of the language."

      which I agree is a correct and meaningful statement, but then you write:

      "Nevertheless, in physical sciences, we can identify the theory with the syntax and the experiment/observation with the semantics (e.g. [8])."*

      which is a statement of which I cannot agree. If semantics (meaning) can be identified with experiments/observations (data) alone, then we would have no need for syntax (theory). Experiments/observations can only be the basis and support for a particular theory. The meaning derived from any theory then comes from its interpretation. Meaning can never be derived from data alone, which I believe that you fully agree, since your examples show how meaning changes as the theory changes. But one theory can have several differing interpretations.

      IMO the meaning behind of the quantum mechanical description of nature is not yet fully understood. This is due to the fact that, even though QM gives a correct mathematical description of experimental results and observations, it still has several different interpretations, none of which is quite satisfactory to give us full understanding of the microscopic nature of reality. It may be that a deeper understanding will never be achieved, and this is a consequence of the true nature of microscopic reality. It is my hope that this is not true.

      If I have misunderstood your statement * above, please let me know.

      BTW, you wrote:

      "Para-phrasing Augustus de Morgan(7 ), I could say that today the two eyes of the knowledge are philosophy and science: scientists remove the philosophical eye, while philosophers remove the scientific eye, each believing that it sees better with one eye than with two."

      This statement is a true gem. IMO philosophy is where theory meets interpretation!

      Best Regards,

      Dan

        Dear Dan,

        thanks a lot for your kind note. Let me to answer you with an example. Please consider a dictionary: it is made of words and their semantic field. Pure semantics. But it is useless without a syntax that allow you to build sentences. But the syntax is not just a way to link the words, but it restrict the semantic field of words (although misunderstandings are always present). A very simple example, which I published with more information in an old essay (quant-ph/9804040v4) is the following. Try inserting the word "only" in every possible place in the sentence: "I helped Mickey Mouse eat his cheese last week". You will see that already such a simple sentence slightly changes its global meaning.

        Hope it helps.

        Cheers,

        Luigi

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        • Post #19

        Dear Luigi,

        I'm still a little confused. When does interpretation come into the picture? Doesn't it have a major influence on meaning? For example, the sentence:

        You did a really good job last week.

        could have two different global meanings depending on the context and the manner in which it was said to someone. It could have been said with sarcasm or sincerity. One sentence, with completely opposing meanings depending on context and interpretation, yet it has the same semantics and syntax. Is this not correct? Believe me, I am misunderstood all the time, so I should be an expert. :)

        Isn't this why when people communicate via these forums, sometimes it's necessary to add a :) or a ;) so the intention of the statement is better understood.

        It seems to me that:

        semantics-->(field of all possible meaning), plus syntax-->(greatly reduced subset of possible meaning), plus interpretation -->(one possible meaning)

        The interpretation doesn't have to be true for this to relation to hold true.

        Have a great day!

        Dan

        P.S. BTW, That last sentence was sincere :)

          Dear Dan,

          you wrote a nice example, but I think that in science you never arrive at only one possible meaning, as in spoken language. Indeed, you noted the need of some extra symbols like smiles. I add that it is often not sufficient, because we - human beings - have the unconscious that always elaborate (obviously in an unknown way) what we read or hear. The unconscious itself is structured as a language, as found by the French psychoanalyst Jaques Lacan. If you write an offense by joke and add a :), the could be anyway one reader who believe you are not joking, because he/she does not believe to the smile.

          The same occurs for science. You can make your measurements, giving a meaning to some physical quantities. Then, you can elaborate a theory linking all these quantities and then having a global picture. But each human being will give to this complex of things different "interpretations". I think that two human beings will never fully agree on an interpretation. They can agree on certain details and be satisfied of this partial agreement. But I think that if they dig into their thoughts, they barely find a full agreement. Perhaps we think to know what is an electron, but if we try writing down its definition, we will barely obtain two similar - not to say equal - sentences.

          This is not so dreadful as it could seem at a first look. We are always forced by social convictions to believe that the misunderstanding is something negative. I do not think so. I think that the misunderstanding is the spring that push human beings to develop new science. New theories were born when there were strong misunderstandings, not when each agreed on a certain interpretation. A theory is no more producing new science when there is a globally full agreement on many details.

          So, by updating your scheme, I can write:

          semantics-->(field of all possible meaning linked to a specific sign), plus syntax-->(link between signs; greatly reduced subset of possible global meaning), plus interpretation -->(if there are several possible meaning, then there is open space for discovery)

          The science of books and articles can deal with the first two. The latter is the spring keeping science alive.

          Thank you for your intriguing comments.

          Luigi

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          • Post #21

          Luigi,

          Extremely well said. Look at how many interpretations just of the meaning of time in the first essay contest. This question has been with us since antiquity, and we still don't have a scientific consensus.

          Quote of the day: "The latter is the spring keeping science alive."

          I couldn't agree more!

          Dan

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          • Post #22

          Dear Luigi,

          Since you are interested in scientific languages, I thought you might be interested in the fundamentally new formalism I have outlined in my essay. The reason you might be interested has to do with the absolutely unique feature of this formalism: its syntax and semantics are congruent.

            Dear Lev,

            thank your for having pointed to me your essay, which is indeed interesting. I agree with you that it is necessary to avoid the spatialization of time, although you later write about "irreversible streams" and offer again spatial representation of time (a stream is indeed a spatial representation). Instead, I think to time more like as a "cut" into a space of events (see quant-ph/9804040, pag. 13), a concept on which I am still working.

            You write that the key question is the "transition from the point-based representation to the structural representation". Well, a very clear example of this "structural representation" is the Reimannian geometry, which is based on the relationships between points. This was indeed the power of the work of Reimann and later Ricci-Curbastro, which resulted evident in the application of the general relativity, where the need to measure something continuously changing, as it occurs in an accelerated frame, made it useless the cartesian geometry.

            May I suggest you also to have a look at the work by C. Rovelli, "Relational quantum mechanics", International Journal of Theoretical Physics 35, (1996), 1637. Moreover, I think you might find very interesting for your studies also the essay by F. Markopolou, "Space does not exist, so time can", Third Prize of the FQXi 2008 Essay Contest "The nature of time" (arXiv:0909.1861). She also proposed a time-only based physics, although at a level below the Planck scale.

            Good luck with your essay in the contest!

            Cheers,

            Luigi

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            • Post #24

            "I agree with you that it is necessary to avoid the spatialization of time, although you later write about "irreversible streams" and offer again spatial representation of time (a stream is indeed a spatial representation)."

            Dear Luigi,

            Thank you for your comments!

            However, it appears you *completely* misunderstood the proposed form of representation. The "irreversible stream of events" is a *verbal description* of the proposed formal representation "struct", while you interpreted this verbal description in some geometric/spatial context.

            My best wishes,

            --Lev

            Dear Lev,

            if you want apples, but ask for strawberries, then you cannot complain if people give you the latter. You are giving me one fine example to support my essay, i.e. words are important. When you want to describe a theory, you have to pay attention to the words. What you simply call "verbal description" is indeed part of the theory, necessary to understand and not something detached or useless artifact.

            Ciao,

            Luigi

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            • Post #26

            Dear Luigi,

            Why cannot the "irreversible stream of events" be understood outside the context of space, as I intended it?

            • [deleted]

            • Post #27

            Dear Luigi,

            Since one of the meanings of "stream" is quite abstract (e.g. a steady stream of abuse, complaints, etc.), I find it quite ironic that your spatial bias in interpreting "stream" supports my observation on the pervasiveness of spatial bias in physics discussed in section 2 of my essay.

            My best wishes,

            --Lev

            5 days later

            Luigi,

            Interesting and thoughtful read. We can't know reality and language seems a feeble means to describe it.

            Jim Hoover

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              • Post #29

              Well done, Luigi! I agree with you on the identity between mathematics and linguistics. Ditto on the lack of one-to-one mapping between semantics and syntax -- which I interpret as the independence of language and meaning.

              All in all, you produce a pleasing blend of philosophy and physics, without confusing the philosophy with the physics.

              I hope you get a chance to read my essay entry as well.

              Best,

              Tom