Dear Steve,

You asked: "who was the best rationalist, the most rational and logic between these persons,

Dedekind, Cantor,Riemann,Gauss,Poincarré,Pierce,Euler,Stern,Dirichlet,Hilbert

."

Among my favorites are Euclid, Galilei, Euler, and many others also including Peirce. The latter stands for what the other you mentioned made or considered outdated.

When I wrote pre-Dedekind mathematics, this was a questionable simplification. While I found the old and physically correct Euclidean notion of number still maintained up to the time of Dedekind, its mathematical mutilation to just a single point begun earlier. Let me consider the row Gauss, Riemann, Stern, Dirichlet, Dedekind, Cantor, Poincaré, Hilbert.

The book by Nahin to which Edwin Klingman pointed me made me aware of even elder roots. My admiration for Gauss has become overshadowed when I got aware of his arrogance. More factually, I dislike that he promoted the complex plane, which goes back to Wallis, Wesse, Argand, and Hamilton, without to stress that it is not accessible via Euler's identity but via an omission.

I see Riemann, Cauchy and others preferring to create pure mathematics that neglects the link with its application in physics. What about Moritz Stern, I did not find him mentioned in literature that describes the origin of set theory. While Dirichlet was lacking a solid education, he was nonetheless very influential in particular on Dedekind. Dedekind on his part managed to cautiously and elegantly advertise what I consider a clever seemingly rigorous self-deception. Frankly admitted having no evidence he kindly asked to nonetheless believe him. While G. Cantor had the same intention, he managed to provide stunning evidences and get a nimbus of a genius. Poincaré is told having called Cantor a charlatan. Maybe, he was not quite wrong in that. I like Hilbert's transformation. Hilbert was very disappointed when his successor Hermann Weyl rejected large parts of set theory. In all I see Hilbert's influence on physics with very mixed feelings. It was Hilbert who denied for mathematical reason that past and future are fundamentally different from each other.

Regards,

Eckard

Thank you very much dear Eckard for this beautiful aswer and explaination.Me My Favorites are Borh, Newton , Gallilei and Euler.

I agree about the works of Pierce, it's very inetersting and relevant, as what the rational logic will be always the best road.

The interpretations of the physicality can be made by maths if and only if the real domains are inserted with their pure finite series.

In all case, you are a real searcher of truths and truth.Thanks for that and for your knowledges.

Best Regards

Steve

Eckard

O posted a reply on my page but it didn't seem to go through so I will post it here.

Yes I read your essay but I confess I did not give it proper thought the first time. I apologize to you for my posting as it was not well taken and you are absolutely correct in being disturbed.Your essay is very good and your points well taken.I shall endeavor to read further essays more carefully.

Tom Wagner

    Dear Eckard

    I am sure which might be the better place to submit a post so I am submitting to both our sites.

    Thank you for alerting me as to the rating system of which I was unaware. I will certainly now reread your essay (I have been fighting some deadlines here so I could not give this entire project the attention I would like. I am now going to take the time to read some of the other essays as the interplay between those of us who entered essays seems to be the most interesting part of this whole experience.

    Tom Wagner

    Dear Tom Wagner,

    Having read several essays, I realized that almost nobody besides me addressed not merely continuous vs. discrete but literally analog vs. digital models.

    Accordingly most readers of my essay did perhaps not understand why I consider already DEQs the first step into ambiguity and complex representation twice redundant. The reasons for me to thoroughly deal with history of mathematics were mainly paradoxes not just in physics but also already in mathematics.

    I pondered about the possibility to restrict the scope of my essay as not to lose all readers. However, even if I was not in position to explain in detail how the many uncommon alternatives to established tenets are interrelated, this mutual dependency is important.

    What about the chance of getting these alternatives taken seriously, I so far hoped in vain for arguments that challenge me, and I can imagine how FQXi cautiously anticipates reactions of those who are definitely unhappy with what they will feel wrong and an attack on their theories. Not all posts are immediately shown. My votes did not change the indicated rates and numbers of public votes. Nonetheless I highly appreciate the opportunity to take part in a polite factual discussion without taboos.

    On the other hand, I consider most of the alternatives well founded, and I expect the outcome of LHC providing further support for my criticism. In the meantime, I can only collect further indications.

    Regards,

    Eckard

    Dear Eckard

    I have reread your essay and I do have a better picture of what you are saying. While I do have a fair layman's grasp of the study sub-atomic particles I do not possess the sophistication nor the experience in such matters to allow me to engage in a meaningful debate. I plan to read it again as there is much included that stimulates ideas.

    I was struck by your reference to Sommerfeld on page four. When he states that no wave is reflected from infinity in finite time sounds a bit like the notion that a moving object cannot transverse an infinite number of points in a finite amount of time. Be that as it may, I am more interest in the next statement, Standing waves are strictly speaking approximations.

    A standing wave is a very definable and precise physical phenomenon. It is the initiator of most and perhaps all sound. This can best be seen in a musical example. More than half a century ago, Frederick Saunders wrote an article about the physics of music for Scientific American. This article had more errors and misconceptions that I have ever seen in one article. Saunders was a noted figure in the acoustical world, but physicists are only human (at least most of them are).

    One false assumption that most people make about the generation of a music as sound, and I use Saunder's example of an instrument such as a clarinet or an oboe, is that it is the movement of the traveling longitudinal wave that transverses the from the mouthpiece to either the end of the instrument or to the first open key actually creates the sound.. A conjugate is returned and wave moves back and forth through the instrument.

    Saunders makes the statement that it is the air that flows in and out of the finger holes that creates the sound. He then went on to state the fundamental is the only note whose sound goes out of the end of the instrument. If this were to be true then why do they put bells on both clarinets and oboes if they only affect a single note?

    The movement of the traveling wave back and forth sets up the frequency of the tone. The structure of the sound begins in the reed of either instrument. This is fed from the mouthpiece to the sides of the instrument. The movement of the air creates a classic standing wave, which is modified by the information residing on the sides. The severe impedance mismatch between the air and the materials from which an instrument is created means that the body of any instrument contributes little to the sound we hear. The primary interface that creates the sound lies across the plane of the open end of the instrument. This is why a bell increases the volume of the sound; it increases the area of interface.

    This is true of most instruments. The standing wave that forms in the body of most instruments is a resonance. Perhaps the biggest obstacle in understanding sound is the lack of understanding that a vibration and a resonance are two related but decidedly different things. Any material with some elastic properties will resonate to any frequency. Only if the resonance is near to the overtone structure of the resonating material will that material vibrate. On the other hand, a vibration is necessary to create the resonance initially. Both the vibration and the resonance are digital.

    Sound is not a single isolated occurrence; it is a process that ends in the Organ of Corti. The Organ of Corti is a fluid filled canal in the cochlea, which houses the hair cells that stimulate the nerves to the brain. The final argument for hearing being a discrete process is that the messages the nerves send to the brain are in the form of discrete pulses. They respond to an increase in amplitude by sending more pulses per unit time.

    Since all of the nerves that send data to the brain are quite the same we have to wonder if all sensations are transmitted to brain as discrete pulses. While I agree that the brain is not necessarily just a big computer we have to be aware of the fact that the complex of nerves that address the brain do behave a bit like a computer bus and the pulses are, in effect, bit patterns.

    Thanks for a very provocative essay.

    Tom Wagner

      Dear Tom Wagner,

      Please do not take it amiss that I added Wagner. Tom alone is perhaps a too frequent name. You need not telling me acoustics. While my dissertation, forty years ago, was a comparative study of power electronics for arc welding, the superiority of welding by ear challenged me. Maybe you know the English professor and self declared pop star Chris Plack. It was he who told me that there is a Steven Greenberg of ICSI Berkely who uttered similar ideas on the mechanism of hearing as I suggested. The latter argued correctly that a frequency analysis alone could not explain the astonishing performance of hearing. For instance, onset is utterly important. Steven Greenberg organized together with Malcolm Slaney of Stanford an Advanced Study Institute on Computational Hearing in 1998 in Il Ciocco, Tuscany, and invited me to take part. Here I met virtually all important experts on hearing. Since then I thoroughly dealt with auditory function.

      Certainly you know the huge list that was initiated by Al Bregman and is maintained by Dan Ellis. Al Bergman asked for altruists as to get his list rid of too controversial discussions. Jont Allen and I each provided a forum.

      I intended to find out how the extraction of temporal features from sound might work and how to explain why the spectrogram has so many shortcomings. In the end I got increasingly aware of a cardinal mistake in theory of signal processing:

      Complex analysis and inclusion of void future data is a detour.

      Meanwhile I also got familiar with many details of the physiology of the auditory pathway up to A1. In Magdeburg we have a Leibniz Institute of Neurobiology. Moreover I regularly attended the annual meetings of DAGA (German Acoustics Society) and read JASA as well as ARLO papers. Currently I am just participating in a list on Cochlear Amplifier by Matt Flax.

      What about my statement that standing waves are strictly speaking an approximation, I should add that I was teaching fundamentals of electrical engineering for decades. So you may consider me a professional in this field.

      You wrote: "A standing wave is a very definable and precise physical phenomenon." What I meant refers to the fact that every signal in reality has a beginning and an end. We may describe it as a superposition of a transient and a stationary component. Neglect of the former is an approximation.

      If I did not sufficiently answer your question, please do not hesitate asking again. Questions by laymen are often valuable. We need not be able to follow for instance Lawrence Crowell as to find out why the theory of "relativity" and non-relativistic quantum mechanics do not fit together, why quantum computing does not work, and why so far neither the Higgs boson nor SUSY were experimentally confirmed.

      Regards,

      Eckard

      Regards,

      Eckard

      Dear Eckard,

      I wish I had a greater knowledge of the things you discuss in your essay. I think you are doing an important job of looking at the mathematics that is used to describe reality and what it really means to be continuous or discreet , analogue or digital. For models to be -realistic- these considerations need to be made. It is a very different approach to the other essays I have read here and a valuable direction of investigation. Because of my non mathematical background it is an essay that I will have to reread a number of times and digest slowly.

      I will admit that the thought "what do we -really- mean by continuous or discreet, analogue or digital?" did pop into my mind but having a huge body of content discussing reality there we was not room to also thoroughly consider that in my essay. I think you are doing that. I touched on it with the film photography. Which may be talked about as an analogue process but the film does have a chemical structure and therefore it is individual grains that change color or not.

      I did notice that Eugene Klingman in this thread mentioned the usefulness of having i orthogonal to a surface. IMO There is unseen spatial change over time, which is not visible from the perspective of the observer, at the same scale as the observed object. The direction of that change can not be a direction that exists within the 3 dimensional spatial structure of the observer's individual reference frame. It is an other direction. So therefore it can not be represented as a real direction or measurement because it is not seen and so is not measurable like a "real" distance.

      Your support has not gone unnoticed and is very much appreciated.I do hope your ideas get the attention consideration they deserve.

      Georgina.

        Dear Eckard

        I was hoping to see a response to my post above. The more rigorous logical analysis is in a post I've just made to Tom in support of Georgina in the blogs (Time travel) but repeated in my string. I hope you'll look, as it identified conceptually and logically where our understanding and application of maths and SR was incorrect.

        I note I haven't scored yours yet and will do so now with the far higher one it deserves, as time is running out. I do hope you will agree mine deserves the same, if you haven't done so yet.

        Very best wishes.

        Peter

          Dear Paul,

          In my understanding, foundational questions should not just include FOM (fundamentals of mathematics) but demand some clarification in FOM even if corrections might be painful to those mathematicians to whom aleph is a gospel and set theory the alpha and omega alias infinity of mathematics. I agree not just with David Joice in that the good old Euclidean notion number was abandoned in the 19th century. So far I seem to be the first one who makes this an issue. Cantor's "counterintuitive" infinities beyond infinity provoked distrust, and they got even used as to enforce purely formal thinking. I do not intend being considered one more crank who tries to disprove Cantor or Einstein. Having dealt with the foundations of the foundations, I see the necessity for tiny but very basic resurrections.

          When I tried to explain why discrete and in particular digital models are superior, I did not hide that any belonging abstraction and in particular linearizing implies a loss of realism. I do not yet see any possibility to decide whether or not the world is anyhow discrete at the lowest level. However, most likely such lower end of our scales for temporal and spatial distance would be as useless as an upper end. I never dealt with or believed in the big bang.

          Already when I was a child, I did not understand those who spoke of blowing up a point. To me numbers and continua are likewise abstract notions that do not have exact correlates in nature unless we define for instance how to count a pregnant cow. My Fig. 1 might illustrate how to imagine discrete values to be seen in a continuous function and how a non-linear transformation changes the scales. When I heard for the first time the expression negative signal to noise ratio, I was confused. How can it be negative? The answer is simple: SNR is usually given in dB.

          Best regards,

          Eckard

          Dear Eckard,

          I enjoyed the ideas in this essay. We are very much on the same line. Quantities are related to objects, negative and complex numbers are useful because they represent orientations of real objects. They represent common sense reality, nothing magical about them. We could do without complex numbers and replace them with their 3D analogs, the more powerful quaternions.

          I remember you also used examples of auditory perception in last year's essay to make your point.

          I especially liked the sentences:

          "Strictly speaking there are neither absolutely continuous nor absolutely discrete signals, because any tangible thing is finite."

          "Even begin and end of an animal's life are continuous while irreversible processes."

          "Peas are preferably treated as if they were uncountable. Uncountable liquids are measured in terms of countable gallons."

          "Both the foundations of mathematics and, to a larger extent, basic interpretations of implication for physics are not yet as mature as possible."

          "...unfortunately common identification of a number with just one point instead of the distance between zero and a virtual limit point..."

          "Foundational pragmatism outperforms pseudo-foundational formalism"

          Best wishes for this contest,

          Arjen

            Dear Georgina,

            Be not worried if I got anonymous. It costs me time to login. Nonetheless I did so again. The system seems to tend logging me out.

            I apologize for not reading most of the many responses you got. Admittedly I am a bit disappointed because you did not as clearly issue against spacetime as I hoped you to do.

            Edwin Klingman asked me about the same as did you: How to interpret ict and ih. Concerning the latter see my essay. What about ict and spacetime, I seem to be the only one here who claims that physics must get rid of the Janus head of a mathematics that claims to fit reality from minus infinity to plus infinity. This would not even fit to the big bang.

            I do not understand what exactly you meant with spatial change over time. Engineers like me have to understand their tools. Complex plane is a tool to me, not an extension of numbers. Already Bombelli wrote that a+bi always comes together with its complex conjugate a-bi. In order to get only a+bi, one has to arbitrarily omit the latter. Of course, complex calculus is utterly advantageous - provided one does either not forget to go back into the domain of reality or a complex solution can reasonably be interpreted, e.g. complex impedance Z = R +i omega L.

            Best regards,

            Eckard

            Dear Arjen,

            Even John Baez confirmed in principle that quantum physics can equivalently be expressed in terms of real or complex numbers, and quaternions and octonions.

            However, so far he did not even mention the - as I maintain - reasonable tailor-made description in terms or only positive real numbers (R).

            My argument is simple: Any finite interval in R can be completely shifted into R, and this shift merely reverses the original physical relationship. For instance, any analysis of measured data has nothing to do with what will possibly happen after the measurement.

            Some consequences imply a lot. For instance, there is presumably no a priori given block of spacetime, no Higgs boson and no SUSY. MP3 works well with cosine transformation. This does however not mean that negative and complex numbers are unnecessary. On the contrary, they are utterly advantageous if correctly used and interpreted.

            Regards,

            Eckard

            Dear Peter,

            I did not yet read what you just wrote in your string. Time travel is impossible to me. What about the somewhat simplistic explanation you gave by means the metaphor of a river, it did not yet immediately convince me. With acoustic waves in a single medium one can also not exceed the velocity of sound by means of superposition.

            You might read what Tom Van Flandern wrote: "Is faster-than-ligth propagation allowed by the laws of physics?" and "Lorentz Contraction" in http://metaresearch.org/cosmology/gravity/LR.asp .

            Does it agree with your ideas? I see it agreeable with logic and all pertaining experiments I am aware of. It also seems to agree with the many convincing arguments collected by Ekkehard Friebe.

            Yan Flandern recognizes a universal time, a universal instant of now. Lorentz transformation works just one way and therefore without paradoxes. Minkowski metric seems to loose its basis. Physics becomes less mystic, and my touch stone seems to work: We do perhaps no longer need ict.

            Regards,

            Eckard

            Dear Eckard,

            I am very pleased with your new found popularity. Hope your essay makes it to the panel, as it appears it will. I am equally (if not even more) pleased, but not with my rating position (38) of my essay. But rather, by a very significant result I just posted yesterday. I consider you a friend and a supporter. So I just had to tell you of this directly.

            Two very key assumptions in physics (dating back to Einstein) are

            1)The constant speed of light (CSL)

            2)The Photon Hypothesis (PH)

            The first lead to Relativity, while the second lead eventually to Quantum Physics.

            In my very short paper "If the speed of light is constant, then light is a wave" I give a simple mathematical proof that CSL contradicts PH.

            I look forward to your always insightful comments.

            Best Wishes,

            Constantinos

              Dear Eckard,

              I really have not thought enough about these questions of the fundamentals of mathematics and how best to use mathematics to model reality. Which is one of the reasons I am very glad that you are.

              I was just trying to say that I think there may be a legitimate use for i as explained and hopefully clarified below.

              In my essay I have tried to show that space-time mathematics relates only to the recieved image of reality and incorporated temporal distortion. There is no change within the space-time model as it is a static geometric model, where time is a part of the geometry.

              However to have casality and passage of time there has to be a foundational reality where there is spatial change giving a sequence of earlier and later. Hence time appears as earlier and later in a sequence of spatial arrangements or positions. The spatial sequence is Mc Taggarts C series; the earlier later passage of time is B series; (space-time) past , present future expereince is Mc Taggart A series time. See his paper on the unreality of time in my references.

              So if One wishes to have that passage of time type change and -also- relate this to what is observed (in static space-time) one needs to have a change of position that can not be represented within the 3 spatial dimensions of space-time and that is a spatial distance that can not be a "real" measurement of distance because it can not be observed as a distance, within the observers scale and frame of reference.

              Dear Constantinos,

              While I maintain my support for you, I would like to clarify that the constant speed of light does not date back to Einstein but largely to Maxwell. Likewise the principle of relativity does not date back to Einstein but at least to Galilei. Planck's quantum (1900) predates Einstein's (1905) PH. Planck's appreciation might be to blame for his decision as editor to accept Einstein's paper "Zur Elektrodynamik bewegter Koerper" which omits any reference to Poincaré.

              Best regards,

              Eckard

              Dear Georgina,

              Use of i is of course legitimate. I trained a lot of students to use it. However, all physics except for quantum theory can in principle be reduced to differential equations instead. More precisely, the latter can be abstracted from original integral relationships as I tried to explain. Pauli raised the question why quantum mechanics is the only lonely discipline for which i is essential. I gave references that demonstrate his mysticism.

              I appreciate your insight that spacetime cannot be a physical reality. I would not call the Doppler effect a temporal distortion, and I maintain: Future data cannot be perceived.

              What about Mc Taggart, I do not consider him worth mentioning if we intend to explain to ordinary people what everybody understands anyway, the distinction between past and future. It is just the unrealistic model of blocktime that causes trouble. You are quite right calling it "a static geometric model".

              Only elapsed time can be measured.

              Regards,

              Eckard

              Thanks for that historical clarification, Eckard. I am always impressed by your vast knowledge and your deep insights. And that is the reason I seek your comments on the result I linked in my last post.

              I am aware that Maxwell's equations (considering light as a wave) determine that the speed of light is a constant. My just posted result does the opposite. With the assumption that the speed of light is constant, I mathematically demonstrate that light must be a wave. Thus, under all circumstances, light is a wave. In my view, this contradicts the Photon Hypothesis and the 'physical view' it lead to. It makes a strong case for a continuous universe.

              Good luck,

              Constantinos