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Dear Eckard,

Thanks for confirming! I do value your support of my attitude. Do you equally confirm my many mathematical derivations in my essay resulting from this attitude? If not, which one specifically you have questions about? My Planck's Law derivation? The equivalence of Boltzmann's entropy equation to Planck's Law? The mathematically argued connection between entropy and time? My interpretation of The Second Law to say that 'all physical processes (events) need a positive duration of time to occur'? My existence argument of Planck's constant and what it really means? Or something else of the many results in my essay too numerous to list in this post?

I take all your advice seriously and reflect on it. Reflect on the results I have in earnest put forth. All are mathematically argued. Some may surprise you.

All the best,

Constantinos

Dear Constantinos,

Perhaps I understand your unhappiness. I am sorry, I feel not in position to judge your mathematical work. Even if I did endorse it, we both together would certainly not manage to convince editors of refereed journals that it is not just correct but even a Physis and a Rosetta stone.

I admit a suspicion of mine: You certainly know that Einstein was influenced by Boltzmann when he agreed with Ritz to not agree. Ritz meant: Future cannot influence past. Even the late Einstein denied the separation between "past, present and future". I consider Ritz correct in this case, and I am arguing that the idea of a spacetime that includes the past and likewise the future is anticipatory and reflects a fatalistic attitude.

If I recall correctly, Georgina Parry shared Einstein's presentist view while she nonetheless denies the reality of spacetime. I did not yet take the time to thoroughly analyze her essay and the belonging discussion.

Anyway, I suspect that there might be hidden mistakes around the use of probabilities and distributions. Did you read the essay by Joel H. Meyer, a Medical Doctor? In a previous contest I mentioned an obviously unrealistic result by Gompf et al. as a reason for me to distrust single electron counting.

Let's ahow that we are not yet too old as to find out mistakes.

Good luck to us both,

Eckard

Dear Peter,

I do not put your ideas concerning c/n in question because my focus is directed only on the very basic reasoning to be read in Einstein's 1905 paper on electrodynamics, more precisely it is devoted to the assumed procedure of synchronization. I am anyway not competent in the huge field of plasma physics. I merely dealt with high pressure welding arcs with a lot of opaque metal vapor and temperatures in the range of several thousand K. And I abstain from swallowing guesses how large, how old, and how ionized the whole universe might be.

So far I found out that the idea of round-trip synchronization might originate from Poincaré 1898. I consider it the basis for Minkowski metric, and I suspect it being at least inappropriate if not simply wrong.

In order to clarify the matter we need at first no speculations on how to interpret more or less belonging experiments. We only need logical reasoning.

Regards,

Eckard

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John Baez is a good mathematician but the realism is not always his priority.

Eckard you are surprising. I was right , you are the real teacher here, the best for me.sincerely.

Regarsd

Steve

Hi Eckard

What disappoints and confuses me most is that you can't see the pure logical reasoning my hypothesis is based upon, and it's very important consequences.

Secondly your apparent unwillingness to research that which you question, but willingness to remain without that knowledge! If you follow the links (or simply Google!) you'll find that the density and extent of ionised particles (plasma) is not really in any contention until a third approximation. The 19th Feb new scientist (p18) shows it's (extraordinary to those who haven't researched it) domain and capability as the surface fine structure of all matter, (doi:10.1021/nl103408h) and the latest Nature refers to galaxies with around 300Bn Solar masses of plasma halo (i.e. a little above average) being most likely to become 'starburst galaxies. You must agree we will never find answers if we're poorly informed and harbour too many doubts.

You talk of 'speculation'. The reason I have researched so carefully and comprehensively is to remove that speculation (though it will never be non zero). Logical reasoning needs the firm foundation of good postulates.

You must try to see it from my viewpoint. Having done that I now only come across people who haven't bothered to do it, but think it reasonable to accuse me of guesses and speculation!!!

Frankly it is clear science will never progress while people think it reasonable to do that, and I feel very let down that you seem to be happy to join them Eckard! I thought far more of your scientific rigour.

Are you really not prepared to simply check the evidence base and logic of any parts of my work you query? At the end of it is the solution you (and many others) search for, but if it can be shown wrong I will be very happy too! I only ask that it is assessed scientifically, not by the lazy saying; "I can't be bothered to check but think 'this' ..which doesn't quite match so I expect you're just speculating so will ignore your thesis".

You recognise we need logical reasoning then ignore it! That is quite insulting and I really can't believe you recognise that is what you are doing, or do you?.

Peter

    Dear Peter,

    Please calm down. I never accused you of guesses and speculation. I just refused to endorse something I am not in position to judge. I am sure that your essay and the additional links will be of interest for many experts. I merely fear, your sometimes empathic style could possibly deter cautious referees.

    Let me clarify: So far I do not even consider the Big Bang a proven fact but merely a hypothesis. I do not expect any possibility to get reliable knowledge on how old or how large the universe might be.

    My reasoning, my experience and my gut feeling tell me that the claim by Nimtz having measured propagation of signals with a velocity in excess of c is undoubtedly based on mistakes.

    You will certainly agree that opposition to SR is reasonable despite of its allegedly overwhelming experimental confirmation. Time will tell whether your reasoning is correct. If I understood you correctly, you wrote you do not need the Lorentz transformation. So far I do not see an immediate contradiction between this statement and my objection against the ABA synchronization. Admittedly, a symmetrical (Galilean) synchronization alone does not yet answer all questions.

    I am reading some pertaining books.

    Regards,

    Eckard

    Dear Dough,

    Thank you very much for the link that promises an easy understanding of the notion torsor. Hopefully Steve was not quite wrong when he praised me as a good teacher. At the first glimpse John Baez seems rather to resemble such teachers like Cauchy and Kronecker although he starts with easily understandable examples. It does not matter much that he wrongly assumes that one cannot measure voltage but merely differences of it. Actually voltage is already the difference between two potentials.

    Engineers and physicists might smile and wonder how mathematics now rediscovered the unilateral quantities which were so far called semi-groups.

    Moreover, I feel a bit bewildered by a lot of explicit and implicit exclamation marks.

    Maybe my aversion against category theory is premature. In this case we should be grateful to John Baez as an interpreter.

    Papers like "Topos Theoretic Aspects of Semigroup Actions" by Funk and Hofstra are less digestible for non-mathematicians.

    Now it should become obvious how my hopefully largely sufficient suggestions are mutually interrelated while at variance from the very beginning with a quite different and highly artificial set theoretic and even category theoretic approach.

    Regards,

    Eckard

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    Dear Eckard,

    Your criticism is always well intended, wise and helpful. I consider you a friend and a supporter. We share, along with many others in this forum, many misgivings on the current 'state of physics'. And we seek earnestly to 'find meaning where meaning is not found'. Whereas you look for such by deeply examining the math used in physics, I tend to question the 'physical view' of physics.

    But I have come around more to your view that there may be something amiss in the way math is used in physics. Math abstracts too much from physics. Unwittingly, we may be drawing wrong conclusions. Certainly, 'point masses' may be a problem. But also spacetime, as many have argued in this forum. My misgivings about a spacetime continuum is that it appears to me that this viollates basic laws of thermodynamics. In my humble opinion, it may be incorrect to 'instantiate' physical events by (x,y,z,t). I believe thermodynamics requires that physical events have 'extention' in space and 'duration' of time.

    This necessity of thermodynamics takes many forms. In my explanation of the double-slit experiment I argue that 'there is an accumulation of energy over some duration of time before manifestation of energy'. This view also appears in my mathematical derivation of Planck's Law. I also demonstrate this in my essay with the mathematical relationship I derive between thermodynamic entropy and time. And you have argued in the past that this idea may also explain the Gompf et al. false measurements.

    Eckard, it is my belief that the only mathematics we should apply to physics is that which describes the 'interaction of measurement'. My derivation of Planck's Law is such. No wonder it is so remarkably accurate. Mathematical models of the Universe may contain abstractions that are unrealistic.

    Constantinos

    Dear Constantinos,

    Does "math abstract too much from physics"? No. I rather see all those morons or charlatans who confuse an abstract model with the object from which it was abstracted. Having experiences an even worse rating now, I pretend ensuring all fans of the Greatest that he is of course an exception. I am here still waiting for a miracle, the promised comments by Tejinder Singh.

    I appreciate your partial agreement with my criticism, and I also agree with your thermodynamic argument against spacetime. Did you read the excellent book by Zeh?

    What about my aversion against what Bourbaki declared foundational to mathematics, a clueless and somewhat sad professor of mathematics pointed me not to Cantor who was obviously let's say exotic but to Weierstrass who got respected after many poor years when he shocked the community with a monster function. Meanwhile I understood the trick. He used the two mutually excluding aspects of infinity simultaneously. In these decades of the 19th century, the good old notion number was redefined with serious consequences from naive set theory to Hausdorff continuum and category theory, affecting physics too.

    I agree on that experiments are touchstones for theories. However, the correct design of experiments and the correct interpretation of the results are crucial.

    Best regards,

    Eckard

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    I think it really, you are very skilling and rational at my opinion.I beleive you must give them a course of rationality and objective realism.It's only simple that this.

    if I learn here it is with the kind of persons as you.Because I am arrogant yes, but I love learn all days.With you I have learned several concepts and ideas and equations.The alephs of Cantor....mainly.Don't change Eckard.

    Best Regards

    Steve

    Dear Dough,

    You wrote: "I have some further comments to make on this subject,... "

    I am curious.

    What about Georg (I consider Moritz more important) Cantor's aleph's, rumor had it that some universities intended to no longer teach set theory. To my best knowledge there is no single application for any aleph except for countably infinite (aleph_0) and uncountable (aleph_1). Moreover I did not find a single tenable evidence, see my Appendix B. Poincaré might be to blame for spacetime. However, it might be correct that he called G. Cantor a charlatan and set theory an illness we will be cured from. I am sorry for hurting the feelings of so many who were trained to see G. Cantor an idol.

    Regards,

    Eckard

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    Dear Eckard,

    You wrote:

    "I am arguing: Real numbers must be understood homogeneous, i.e. without distinction between rational and irrational ones. Only then they are truly essentially different from the rational ones. This requires to admit that numbers of infinite precision within a continuum of such truly "real" numbers cannot be subject to trichotomy. In other words: I consider Dedekind's extension from rational to real numbers reasonable on condition we do not try to enforce trichotomy for the real numbers too. This paradise is elusive."

    Unless I'm missing something, the idea of homogeneous R is acceptable, because any magnitude whatsoever can be set equal to the unit value of R. Thus, what was an irrational magnitude in association with another unit value, can be transformed into a rational magnitude by fiat.

    Of course, as soon as the transformation is made, another set of magnitudes, different from the first, becomes irrational. The process is repeatable ad infinitum. So, why then do we speak of rational and irrational numbers in an absolute sense? A given magnitude may be considered rational or irrational, depending upon our choice of reference. In this sense, geometric magnitudes are relative, not absolute.

    In my opinion, the really ancient (i.e. more ancient than the Greeks) had it right, when they said that, where two quantities exist, one greater than another, then there shall be one greater still. They made no mention of "irrational" magnitudes.

    However, it's not that we can ignore them, or else we wouldn't be having this contest. But the more important question is the one of trichotomy, which the ancients held as fundamental. When we consider that the elements of R have two interpretations, then we can consider the trichotomy of numbers two ways. The first sub-divides the unit number (the quantitative interpretation of number), and the second compares two sets of unit numbers (the operational interpretation of number).

    In the first interpretation, the numbers 1/2 and 2/1 differ by 2 operations, not by 2 units. This is the basis of the concept of octaves, or a doubling/halving operation, we might say. If we double 1/2 once, we get the quantity 1, double it again, we get the quantity 2. Conversely, if we divide 2 into half once, we get the quantity 1, half it again, we get the quantity 1/2. Performing the operation twice in either "direction," shows the symmetry of the numbers, with respect to the number 1.

    In the second interpretation, the numbers 1/2 and 2/1 differ by two units, in a a single comparison operation. We are evaluating them to determine which number is greater than the other number, or if there is no difference between them. In this case, the operation is like the balance scale, rather than the knife, and the quantities are discrete. Although we could choose to include fractions of discrete units, but then we must decide whether or not to include both the equal divisions (i.e. rational parts) of a single unit, and the arbitrary divisions (i.e. irrational parts) of a single unit, or only one of these.

    Choosing to exclude fractions, we can use arbitrary signs (e.g. & -) to indicate our perspective relative to which side of the number 0 we might refer to. However, in this case, we must remember that the number 0 is actually the number 1 again, as in the first interpretation, but with a different meaning.

    This time, the number 1 is both 1 and 0, at the same time. It is interpreted as 0, because 0 represents the result of the comparison evaluation between the two numbers, when there is no difference between them. However, 0 is also interpreted as 1, because 1 means that the relative number of units in the comparison of the two sets is equal. It's just two different ways of regarding the same thing.

    So, dear Eckard, I believe that you are right in that no trichotomy exist in R, natively, but we must recognize that we can clearly employ the elements of R to produce a trichotomy, in at least two ways.

    Sincerely,

    Doug

    Dear Eckard,

    I have definitely enjoyed reading your thought-provoking essay. However I need more time to understand what your eventual conclusion is. Your essay is strong on historical mathematics aspects of the digital versus analog issue, and I learnt new things. But I cannot say that the questiion `digital vs. analog' is meaningful if taken in one whole go to address all of nature - I believe you express that too. Clearly, different phenomena exist that are digital/analog. That is why I have tried to address a specific issue.

    Like I said, I certainly enjoyed reading your knowledgable essay, but I cannot form a view as to your conclusions. I should apologize that I am not saying something more substantial right now ...Cheers ...Tejinder

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      The problem indeed with Cantor as several mathematicians as Mr Baez ..., they do not respect our walls, and limits, they want know with their methods behind these walls.The problem is what the numbers do not exist there, as the time and nor dimensions.That implies that all their conclusions are falses just because they make the same error than Cantor, they do not respect this domain and its limits,they want explain with our physicality a thing without phsyicality.That has no sense of course as the pseudo hidden variables or this and that.....REALISM AND OBJECTIVITY.

      never 1 idea ....but several......always an occahm razzor of rationality.....the idols do not exist.Just works towards our truth.....simple and evident of course.

      Poincarré and Rienmann shall agree I beleive.

      Good luck, you make a good job also Eckard, I have a name for you, the master of the Occham Razzor,don't hesitate to put the equilibrium.

      Regards

      Steve

      Dear Eckard

      You: I would like to add: Even the tiniest piece of the line can even be thought to contain uncountably much of points.

      I agree, as I said the tiniest piece of a line is also a line and it can contain infinite points.

      I wrote: "Well Cantor just showed by induction that there are infinites sets "bigger" than others, but he did say anything about the idea of the infinite."

      Sorry, here I have a mistake, I wanted to say that: "... but he did NOT say anything about the idea of the infinite."

      You: In my Appendix B I disagree with you and also with the mainstream of mathematicians. We need not dealing with the logical splits in Cantor's many utterances concerning what he called merely potential infinity, infinitum creatum sive transfinitum, and infinitum absolutum if we accept with Archimedes and Spinoza infinity as the property that cannot be reached by counting and not exhausted: Addition or subtraction of any quantity to infinity yields infinity.

      I agree with you. In fact, lately, I am starting to think that the infinite is just an illusion.

      Israel

      Dear Israel,

      I agree that reaching infinity by counting or reaching zero by repetitious splitting is an illusion. This is however only one aspect of infinity, the so called potential (in the sense of unreachable) infinity.

      Many infinite series are converging. The second aspect of infinity is seen from outside and called actual (in the fictitious sense of perfectly reached) infinity. It is complementary to the first one: The actually infinite sum or product of all elements of a converging series is a (fictitious) limit.

      Imagine for instance a square composed of its half the half of the remaining half the half of the latter and so on.

      A famous example for an infinite product was given by Wallis:

      pi/2 = 2/1 . 2/3 . 4/3 . 4/5 . 6/5 . 6/7 . 8/7 ...

      In such a case theoretically all of infinitely many elements are required.

      I consider it also justified to calculate 1/oo=0.

      Regards,

      Eckard

      Dear Steve,

      Do not compare John Baez with the tragic figure Georg Cantor who believed having got his CH directly from god and who suffered from mental illness since 1884 and eventually died in a madhouse because he was unable to provide proofs for his naive ideas.

      John Baez is in position to emphatically endorse in an elegant manner rather than criticize week for week the work by many many others. He should therefore have many friends.

      Georg Cantor declared virtual all great mathematicians and philosophers including Aristotle, Cauchy, Galilei, Gauss, Hegel, v. Helmholtz, Kant, Kronecker, Leibniz, Locke, and Newton opponents of his unique theory.

      Regards,

      Eckard

      Dear Tejinder,

      Thank you very much for responding and hitting the nail on its head. You are quite right: While I did not hesitate to frankly utter some definitely unwelcome implications from my work as an engineer, I gave no direct answer to the topical question. I merely expressed my doubts: I consider it unlikely while not impossible that anything can be reduced to either purely continuous or purely discrete models.

      I preferred first asking myself whether or not pertaining speculations are foundational, and how reliable are theories that could provide a hypothetical answer.

      Let me tell an experience of mine: When I observed retrograde motion of cathode spots in a plasma, I looked into literature and found about 15 mutually excluding explanations. Such situations made me cautious because at best a single one can be correct.

      Having discovered a lot of obvious flaws in various fields, I am focusing on possible mistakes in most fundamental theories. I hope future generations will be better prepared to answer the topical question if e.g. complex quantization and putative symmetries are better understood.

      Kind regards,

      Eckard

      Dear Doug,

      While I agree with nearly all you wrote, I am not sure whether or not you carefully distinguished between R and Q. This distinction is somewhat tricky. There is no reason to question trichotomy in Q.

      Regards,

      Eckard

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      Cantor had as many men due to hormons, a vanity, it's unfortunally in the biological system, Cantor had also as many thinkers and searchers of truths and truth a kind of illumination, a kind of crazzyness, a kind of I don't know. They thought probably that they were a kind of prophet or a kind of elected by God.That's why probably they have some neurological and psychological problems. Mr Baez seems skilling , the problem is not here, I think that the problem is always the people around the interesting persons, we return thus always at the base of this vanity(present in all persons without difference, now of course all people can evolve and be more humble, it's a personal choice as the faith).Many persons are jaleous or think they are always right,prsonally, I am laughing of that because in fact wa re all the same, humans.Now of course many scientists like to be listened or read, or be honored, it's the human nature.It's always the same problem with a kind of beautiful words repeting still and always the same things than in the books...is it essential, perhaps or perhaps no, it is not the question. It exists good and bad people everywhere and just due to a lack of education and still these hormons and this vanity and the monney, this stupidity above the cries of poors. Cantor for me was a philosophe and not a physicist.Newton I prefer or Borh,or Descartes(do you know his beautiful book about the method, I suppose that yes) thanks for making a little difference.Mr Baez is for me first the cousin of a very good singer that I like, second he has a beautiful blog about the category theory where some maths are relevanta bout topos and this and that,that permits the sortings and synchro in computings, it's interesting in all case.I consider him thus as a mathematician skilling and a good inventor of algorythms I suppose.But he is not a phsyicisists.You yes you are a real physicist skilling and a good mathematician , but you aren't a theoretical physicisit. Edwin, dr Layzer, ...them are theoretical phsyicisicts.

      Me I am simply a human, musician , horticultor and without PhD with a small theory, relevant at my humble opinion.Of course some people will love and others shan't like it.It's the life,I prefer of course working with people who agrees and not of course with the others, as all Eckard , as all I make the same simply.The essential is not to show his knowledges(which are in the books) for a kind of vanity but for a total sharing of a new thing(which is not still in the books, the good books of course).

      Spherically yours my friend Eckard the gentlemen

      ps don't change Eckard!

      Steve