Language is a way to tell stories to other people. Mathematics is definitely limited as a language for quantitative reasoning, just as you say.

The spectra of mathematics can describe qualia, but in a different sense than the words of language. For example, blue and yellow are both colors that we commonly see in reflected light because of absorption by pigments. The math of those absorption spectra is straightforward and so math can represent colors with spectra as long as a white spectrum of light from a source illuminates the object. So I still argue that math can add and subtract blue and yellow absorption spectra and math can fully represent the parrot green spectrum in reflected light given a white light source illuminating an object.

However, the word "blue" also communicates more than the spectrum that math calls blue. The word "blue" communicates a lifetime of both singular and shared relational experiences with blue objects and so the word "blue" describes a blue object in relational ways far beyond what a math spectrum represents.

17 days later

Dear Stephen F. Agnew

Our ideas nearly coincide. You say, "Mathematics expresses the relationships between the matter and time of objects and an action principle. Science uses math to represent action as motion in space but all motion is equally well a displacement of an object in time".

My view: Any 'change' in the physical world happens 'by way of motion'; there are no other ways. And, 'motion' is a space- time relation that follows 'mathematical laws'. So all changes in the world follows 'mathematical laws'. The physical world has no 'laws' of its own; it has only some basic 'properties'. Mathematics decides the 'laws', and that is the only role of mathematics in the domain of physics. Please read my essay: A physicalist interpretation of the relation between Physics and Mathematics

    16 days later

    Dear Dr. Agnew,

    I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

    I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

    All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

    Joe Fisher

      Wow, I am really running out of gas on this topic. You may have missed my point, though.

      There are two equal but complementary math representations for action; motion in space with the conjugates of dx and dp and evolution in time with conjugates dt and dm for changes in time and matter.

      It is really only math that allows us to consider these two representations of physical reality. While spacetime is a huge mostly empty universe filled with a few objects of matter, matter time is a universe of time that is nearly filled with the possibilities of objects of matter.

      So far, using space and momentum, it has not been possible to unite gravity and charge forces since the path integrals between GR and QM are so different. By doing path integrals with just matter and time, it is now possible to unite gravity and charge forces. This is because there is an expectation value for proper time.

      Well, mathematics is really only a tool and a very useful tool. This is because there are many physical things that conform very well to math, like counting objects.

      Dear Steve,

      Thank you for reading my essay and for leaving an honestly felt comment about it. Reality is not optional. Only abstraction can be abstractly right or abstractly wrong.

      Do you have a real complete skin surface? Does every single thing you have ever seen in your life have a real complete solid, liquid, or gaseous surface? Can I predict with absolute certainty that every object that will ever come into existence will always have a real complete surface? Yes I can and I do.

      One needs a real surface to practice mathematics on. Please name me one event that mathematics can predict.

      Joe Fisher

        Okay...math can predict the number of cattle that a farmer must give as tax to the government given a tax rate of 1 in 5.

        16 days later

        Steve,

        Glad I got to your essay, I won't get to many. I'm in full agreement with the importance of Fibonacci etc, indeed the spiral concluded a recent video where I tried to show a relation of the charge path... anyway time is short. I would appreciate your comments on it as I know you've been skeptical of charge/EM coupling. VIDEO Time Dependent Redshift.

        I found your 'no chapter' style a little difficult and apparently rambling at first but it worked ok and the message came across well. I'm not quite sure why it's not better rated. Perhaps we need to bow more to the god of mathematics. You may not get time to read mine to score mine but I hope you'll read it and comment anyway.

        Best wishes

        Peter

          Thank-you for your kind remarks. The rating system seems to be based on more of a Monte Carlo type of realization than on any reasoning.

          I watched your video and am always amazed by the significant effort that you put into your DFM plasma. This is something that you obviously believe in very deeply, but DFM could still use a few more quantitative examples.

          The shock fronts of nebula are beautiful shots, but there are very well grounded alternative explanations for these features as supernova remnants. You need something with a little more mystery than a supernova remnant to argue that DFM is useful.

          Well reasoned and enjoyable Steve..

          You started and ended strongly, with a little stretch near the end but a solid finish. I really appreciate learning more about the history of Fibonacci numbers, and I like the application to Galaxy evolution. Many models are unduly complicated but fail to be realistic. I liked your essay overall, and I will have more to say when there is time. Perhaps I'll finish reviewing one or two more before midnight.

          All the Best,

          Jonathan

            I am pleased that at least a few people have read and liked my essay. I realize that my writing is not always the best that it could be. Things that seem simple to me are not always that simple to others.

            I too like simple models and a simple universe built on a few simple axioms. Why no one else can see the simple underlying primitive reality of matter, time, and action is a mystery to me. My naive expectation was since matter time is so simple and has proven to be useful for a variety of problems, that matter time would then be worthy of a more rigorous vetting by the trolls of mainstream science.

            Thus far, that has not proven to be the case.

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