Physics Suffers from Unwarranted Interpretations by Eckard Blumschein

Let's benefit from comparisons; this is Robert McEachern's comment on my essay:

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Quote/ Eckard, I think the title of your essay hits the nail on the head. It is indeed the unwarranted interpretations, slapped onto the equations of mathematical physics, that cause all the problems in understanding the nature of reality.

Where we differ, seems to be that you believe that avoiding the usage of particular mathematical techniques, will solve the problem, whereas I believe that the problem is that mathematical identities have no unique one-to-one physical identity. For example, the statement:a(b+c) = ab+ac, is a mathematical identity, but not a physical identity. The left-hand-side requires one multiplier to construct it physically. But the other side requires two. Another example, pertaining to hearing, is: sin(a)+sin(b)=2sin(0.5[a+b])cos(0.5[a-b])

From this math identity, one might suppose that one could CHOSE to perceptually hear EITHER a superposition (sum) of two tones, or an amplitude modulated single tone (beats). But one CANNOT do that; depending on the frequency separation of the tones, one always perceives one form of the identity, but never the other. The math identity is not a physical identity. Thus, different physical identities, different physical realities, cannot be entirely described by mathematical identities. This is the ultimate reason why entirely different physical "interpretations", can be slapped onto mathematically identical equations. The same thing happens with the Fourier Transforms (and hence superpositions and wave-functions), at the heart of Quantum Mechanics. Physicists remain blissfully ignorant of the fact that Fourier Transforms are mathematically identical to filter banks, not just superpositions of wave-functions. The filter-bank "interpretation" completely eliminates the very existence of wave-functions, and consequently, all the nonsense about wave-function collapse and mysterious superpositions etc.

In both the hearing and QM cases, the cause of the difference between the math and the physical, is the "amplitude detection" of the filter-bank signals being described by the math. /Unquote

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I rather see various unwarranted interpretations. I begun with the interpretation of the notion number, and I omitted e.g. what I consider the misinterpretation of Michelson's 1881/87 null results, see Phipps.

No, I don't focus on a single problem. I collected a treasure of paradoxes from set theory to Special Relativity and beyond on the one hand and sound hints to ways out on the other hand. I never agreed with those who suggested a bijection between reality and abstraction and even ascribed singular points to reality.

What about mathematical identity, could it be you got me wrong? When I revealed time symmetry just an artifact due to careless use of complex calculus, I criticized the confusion between mathematical identities and the TRANSFORMATION into an arbitrarily chosen fictitious complex domain; translation from there back to the adequate immediate picture in real domain is a must.

As you know, I claimed elsewhere to understand hearing not just as formally as do you in terms of Fourier transformation and filter banks but from a more natural physiological perspective with restriction only to already existing data (IR+). If you will read my essay carefully, you will not just find your excellent previous essay quoted; you might also stumble about my seriously meant characterization of functions as unrealistic if they are thought to extend in time from -oo to +oo.

Best,

Eckard

Dear Giovanni,

Let me first try and answer your question. Mister moon was imagined male, lady Luna female; this more or less ideal model of a pretty old point mass in space is not the only one that was repeatedly changed, corrected, explored, and even exploited.

What about rational vs. real numbers, I largely agree with G. Cantor on that rational numbers are discrete, i.e. numerically distinguishable. Real numbers are not altogether numerically distinguishable. Stiefel spoke of a fog, Weyl of a the sauce of continuum. While I would with pleasure call this continuum of real numbers the mathematical one, set theory occupied and mystified the notion mathematical continuum. Therefore I am calling the continuum of the liquid of measures the Peirce continuum or the logical one, something every part of which has parts.

Are there spacial and temporal continua? The attribution of continuity to space or time is reasonable guesswork. I see a more serious problem in the persistently denied fact that elapsed and future times denote essentially different scales. That's why I see spacetime belonging to speculation and Phipps providing light at the end of the tunnel.

With right line you did perhaps mean straight line?

Thank you very much for your good wishes,

Eckard

Dear Joe Fisher,

My essay does neither address gravity nor Hawking. What about spacetime, I prefer attributing it to Poincaré 1904 and Minkowski, and I see its root in a unwarranted guess by Maxwell, Michelson, Lorentz, and others, cf. Phipps. I don't guess that we need dealing e.g. with the GZK paradox in order to question SR.

I agree with you on that reality "is not mathematical". In particular modern mathematics lost connection to common sense.

I am arguing that there is an ignored paradox: Mathematics putatively demands using complex Fourier transformation for frequency analysis, i.e. integration over time from -oo to +oo. Perhaps one must be self-taught like you, just a user of MP3, or a physiologist in order to admit that a real-valued cosine transformation, i.e. integration only over elapsed time, yields the same result except for an unnecessary arbitrarily chosen reference.

I enjoy Leifer's cut between useful and in principle aviodable mathematics.

Eckard Blumschein

Dear Michel,

Thank you in particular for pointing me to pink noise and disagreeing with ubiquitous causality.

I am distinguishing between ubiquitous causality and its only logical alternative of resorting in something supra-natural. This implies to also distinguish between conjectured causality and a naive determinism as exemplified in La Mettrie's "L'Homme machine". Well, there is perhaps no reason why nature shouldn't play dice, but this doesn't contradict to ubiquitous causality.

Having often used non-causal signal processing myself, I feel aware of this as pragmatic sinning against consequent logical correctness.

What about the corner frequency between pink and white noise, I did never deal with this question. So a suspicion of mine might be wrong: I just got aware that the white (higher frequency) part looks irregular as to be expected while the pink (LF) part looks smooth. Maybe, the latter is an artifact of windowing?

Having tried twice to understand your glittering essay, I felt being perhaps too old and also to less familiar with the details as to always get what you meant. When someone else used the expression "lighthearted" I asked him why he hided himself behind humor, and he frankly explained it to me. Why did you invoke moonshine?

Indeed, Schrödinger managed to explained the Hydrogen spectrum without Relativity, and non-Relativistic quantum theory is accepted as serious.

Accordingly I am capitalizing Relativity.

Best,

Eckard

Dear Michel,

Grothendieck's "Esquisse d'un programme" relates to point-set topology, something that my essay puts in question because General topology cannot even perform a symmetrical cut. I am arguing that the distinction between open and closed intervals of real numbers is only justified in the paradise by Cantor and Dedekind. Maybe, Grothendieck disappeared when he got aware of related inconsistencies.

Already Cantor got insane. While I see other possible victims too, I as a pedestrian didn't get aware of tangible practical results of point-set theory so far.

Best,

Eckard

Best,

Eckard

Dear Michel Planat, dear Tim Maudlin,

I hope to manage making my essay a bit more understandable to experts:

What happened to mathematics? Part 1

Georg Cantor's naГЇve transfinite cardinalities have not by chance proved useless despite of evidence that was more or less accepted in 1873 and 1890.

Let's understand the ideal continuum as a directed measure every part of which has parts while a point has no parts, and any amount of points, no matter how "dense" can therefore not constitute a continuum. For the sake of simplicity we may restrict to one continuous dimension: Length means the distance from a point zero of reference to something that refers to a chosen basic measure called one. This agrees with Euclid's definition of number as a measure and with Salviati alias Galileo Galilei who already used the method of bijection when he arrived at the reasonable conclusion that the relations smaller than, equal to, and larger than don't apply for infinite quantities but only to finite quantities: There are not more natural numbers than squares of them. The converse is not true. With infinite quantities Galileo meant infinite series. The Latin word quantus asks for a measure: how large? The distinction between finite and infinite doesn't ask for a quantity but for a quality of a chosen model.

In point set theory the expression "subset of a set" is used instead of "part of continuum", and a pair of points could be interpreted as the measure, a piece of continuum. However, G. Cantor's point sets are thought to be set together of distinct, i.e. zero dimensional, points, not of pairs of points. Although Fraenkel admitted in 1923 that Cantor's naГЇve definition of an infinite point set is logically untenable [ ], there is still no corrected one. The naГЇve set theory has been replaced by bundles of axioms, e.g. ZFC. Nobody so far put the due attention to a seeming trifle: Not just Cantor but also Dedekind gave preference to the archaic pebble-like notion of number instead of Euclid's measure.

A yardstick may illustrate the fundamental difference between both notions of number, see Fig. 1. Modern mathematics follows those who attribute the notion number to pebble-like marked points on it instead of a sum of spaces between points. Imagine the yardstick chopped into single pieces being still immediately adjacent to each other. Then each cut alias point is located exactly in between two pieces.

In modern point set topology a point a is considered embedded into the surroundings a-пЃҐ and a+пЃҐ. This causes trouble in case of a=0 within IR+ and gave rise to tricks like (-1,0)U(0,1)=(-1,1)\{0}, a so called deleted neighborhood.

With the traditional Euclidean notion of number as a measure, a point is something that has no parts and accordingly no measure. Here one cannot perform the numerical distinction of a single point that is embedded within the continuum of real measures. Singular points can then only be addressed in the discontinuous rational measures. Likewise there is no chance to distinguish between open and closed REAL measures, and only non-zero measures can be numerically excluded or added.

Obviously, topology strongly depends on the choice of the notion number.

Best,

Eckard

James,

Thank you for pointing me to isodual mathematics. I will have a look at it.

If you are unbiased looking for more pearls you might find out what is behind the essay of Phipps, and how Renaissance, propagation of ideas, and the experimental method made Europe rapidly superior to Asia.

Eckard

Corrections to part 1:

? in a-? and a? should read epsilon

1873 and 1890 should read 1874 and 1891, respectively

[ ] should read Fraenkel, A: "Einleitung in die Mengenlehre" Springer, Berlin, 1923

Fig. 1 can be described as follows:

0----|----|----|----|----|----|----| yardstick

1 1 1 1 1 1 1 measures between subsequent points

0 1 2 3 4 5 6 7 numbers attributed to subsequent points

|...................6..................| number 6 attributed to six measures

|.........3.......||.......3........| twice three measures

There is no distance between ||

Eckard

Dear Edwin Eugene Klingman,

Thank you for your warm words. I added some corrections to part one of "What happened to mathematics? Part 1" and will add Part 2 soon.

Eckard

Part 2

At the time of Cauchy and Gauss in the middle of 19th century, the plurality of those who were teaching mathematics grew rapidly. Why did Abel see mathematics in a mess? Abel meant its lacking rigorous foundation. While the irrational numbers were well known to be different from the rational ones, it was common practice to ignore this trifle. When Riemann suggested his surfaces already in 1851, he referred to points, not to measures. After Cauchy had defined irrational numbers as limit values attributed to convergent series, it was and it is still tempting to interpret limit-values as limit-points instead of limit-measures and furthermore to logically equate the never-ending procedure that defines a series of quantities with the limit attributed to it.

Among a lot of pre-thinkers of Dedekind and Cantor were not just rather self-taught ones like Bolzano and Dirichlet but also Heine and the utterly influential teacher Weierstrass. Even Cantor's strongest opponent Kronecker shared their intention to make the continuum algebraic.

Dedekind declared the real numbers an extension of the rational ones. Actually we have to interpret the transition from rational to real as an essential extension, as the transition from discrete to continuous, i.e. from quantity to quality. In other words, in contrast to algebraic numbers, real numbers are not numerically distinguished from each other. For instance, 3.14... is a rational number, no matter how many subsequent decimals. Its limit-measure pi is qualitatively different.

Dedekind made two unwarranted claims:

- He postulated that a given irrational number can be subject to the distinction between equal to, larger, or smaller than a given rational number. He admitted; nobody can provide evidence for that.

- He imagined the real line composed of just enough densely located points. While this contradicts to the definition of a point as having no parts and the continuum of real numbers as endlessly divisible, this idea of Dedekind can be rescued by replacing points with infinitesimal measures.

G. Cantor started with the naive idea that there must be more real than rational numbers and spoke of more than countable many (überabzählbar viele) alias transfinite numbers. As did already Galileo he used the method of bijection in order to demonstrate that the infinite amount of natural numbers is sufficient as to count any rational or algebraic irrational constructs. The latter was a surprise that paved the way for publishing his otherwise silly idea despite of rejection by Kronecker already in 1874. While Galileo had plausibly concluded that there are not more natural numbers that their squares because a quantitative comparison is not reasonable for infinite series, Cantor and Dedekind followed the intuition that only counting means (well) ordering from smaller to larger, a view that denies actual infinite non-linear divisibility. Cantor's proofs rested on the assumption that any number must be smaller than, equal to, or larger than a given rational one. Ignoring the possibility of incomparability Cantor's evidence is logically cyclic. Up to now, mathematicians tend to fail understanding what makes real numbers different from rational ones, cf. an admission by Ebbinghaus in his textbook "Numbers".

Fraenkel 1923 reveals the decisive trick in Cantor's 1891 diagonal argument: Cantor assumed that all of infinitely many digits are fixed. Likewise one could fix all of the natural numbers and then show that by adding something that there are evidently more than infinitely many natural numbers: "Infinity plus anything is larger than infinity" ?

Already the word "many" instead of "much of" is misleading: In common sense, an endless amount is not countable. Cantor's "mathematical" notion of being countable contradicts to the traditional understanding. The entity of all natural numbers is not countable. As Archimedes understood, numbers are endless. They are just tools. The allegedly difficult to understand Cantor's Set Theory is easily understand as a useless intentional denial of sound Galilean reasoning.

What was the intention? Why declared the Bourbakis Set Theory the fundamental of mathematics? See above.

Eckard

Aldo Filomeno replied on Apr. 30, 2015 @ 18:28 GMT

... Your essay looks interesting and original... I'm curious to see how you argue that (A), i.e. that the world displays spatiotemporal patterns, is hardly indisputable. How could it be disputed? I took it as a premise of my argument ... (By the way I don't understand your last observation!)

In parentheses he referred to my claim:

"I should add that I maintain that I consider it unjustified to integrate in case of frequency analysis over available past and not yet written future data. Cosine transformation is evidently as good as Fourier transformation except for it omits an arbitrarily chosen zero."

I guess, Aldo accepted that future data are not available in advance. Most likely, he merely objected to my last sentence because real-valued cosine transformation is a particular case of complex Fourier transformation.

While this objection is mathematically correct, the application of Fourier transformation on functions of time requires Heaviside's trick that uses the mirrored past instead of the unknown future in order to make an integration from -oo to +oo feasible.

In other words, Heaviside's trick introduced redundancy and led to seemingly symmetrical results. That's why the complex representation does not at all convey more information except for the arbitrarily chosen phase reference.

So far, nobody could otherwise explain why the usual spectrogram is non-causal, why in practice MPEG coding works well with cosine transformation, how the rectification by OHCs might be possible in complex domain, etc., etc.

Fourier transformation of a function of time or space and before him John Wallis (1616-1703) and after him Einstein just adopted the Parmenidean (fatalistic) philosophy. Fourier was not even wrong because he dealt with a closed heat conduction ring. However, treating time or space as a loop is certainly not warranted.

If Heraclit and Popper are correct then only the past can be described for sure by a spatio-temporal pattern. The future did not yet happen. It is undecided. I share this view although it deviates from the philosophy behind the majority of the essays in this contest including Aldo's up to average fqxi members. Who is correct?

Eckard