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RECENT POSTS IN THIS TOPIC

Eckard Blumschein: on 2/27/20 at 5:38am UTC, wrote John, “… nature is not likely to be adequately described by any one...

Eckard Blumschein: on 2/26/20 at 19:06pm UTC, wrote Dear Robert, Well, when I am suggesting calculate as if there was no...

Robert McEachern: on 2/23/20 at 15:34pm UTC, wrote Eckard, I believe that your claim is valid for minor, evolutionary...

John Cox: on 2/23/20 at 15:27pm UTC, wrote Eckard, that states it quite simply, and nature is not likely to be...

Eckard Blumschein: on 2/23/20 at 7:00am UTC, wrote Dear Robert, Let me explain why I prefer abstaining from use of the...

John Cox: on 2/22/20 at 17:46pm UTC, wrote Robert, "...crude estimates of received energy distributions, which...,...

Robert McEachern: on 2/21/20 at 19:39pm UTC, wrote Eckard, You are correct: "There is no known to me reason to accept that...

Eckard Blumschein: on 2/21/20 at 16:37pm UTC, wrote Dear Robert, I regret having not yet found a new essay by you because you...


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FQXi FORUM
February 28, 2020

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Calculate “as if “… but be careful by Eckard Blumschein [refresh]
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Author Eckard Blumschein wrote on Feb. 4, 2020 @ 18:05 GMT
Essay Abstract

Shut up and calculate according to axiomatically formalized mathematics as if there were no arguments against Hilbert’s hope for general decidability, computability and predictability. However be careful and don’t speculate as if such calculation was realistic or at least logically correct. Hilbert’s trust in the law of excluded middle was formally challenged by Gödel’s incompleteness theorem and Turing’s more practical halting problem. Unseen examples of possible mistakes with relevance to physics will be shown.

Author Bio

Born in 1942 into disastrous ideological mistakes, the author felt safe in devoted R&D and teaching the mathematical basics of EE, although he got aware of imperfections in theories from mathematical physics up to traditional ethics, too. All ten challenging FQXi essay contests provided to him opportunities for learning and for discussing suspected mistakes.

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Edwin Eugene Klingman wrote on Feb. 5, 2020 @ 01:53 GMT
Dear Eckhard Blumschein,

You mentioned that all ten FQXi contests offered opportunity for learning. I have watched your essays become clearer and cleaner (or perhaps I just understood them better as we went along) and I suspect this last essay topic is ideal for you. It's difficult to find the correct word, but I believe that wisdom best describes your understanding expressed in...

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Author Eckard Blumschein replied on Feb. 6, 2020 @ 03:07 GMT
Dear Edwin Eugene Klingman,

When I wrote FOURIER WAS WRONG, I tried to be as careful as possible. I am anxious, maybe, even you did not yet got aware that I am claiming something new and very unwelcome: having found within Théorie Analytique de la Chaleur a very basic mistake with possibly serious consequences.

Let me highly appreciate your support:

“I very much enjoyed your remarks in #8 on the complex number in QM. Whereas many physicists do not appear to understand the points you make in this essay, I find them fascinating and agree with you as I understand them. I have, for several years now focused on the propensity of physicists to project mathematical structure onto physical reality, and then appear to believe that reality exhibits and is constrained by such structure, with "symmetry" being a key example.”

Nobody will be mislead because you wrote #8 instead of §8 and Eckhard instead of Eckard. However, I anticipate getting deliberately ignored by physicists. What about Hausdorff topology, I admit that I just felt encouraged to utter criticism when I was told that topology cannot even perform a symmetrical cut. Being not a mathematician I may be wrong in this field and have to hope for getting convincingly corrected

My very best regards

Eckard Blumschein

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John R. Cox replied on Feb. 6, 2020 @ 19:20 GMT
Bravo Eckard,

and I can add little to Ed's accolades. You say you are no mathematician but you have always had me fooled, and I am only just understanding enough of what mathematics IS to appreciate it.

Your essay should be awarded the full 1/3 weight of scoring for relevance by the judges, for if not then none other should be. I've bookmarked it on my reader as a favorite, there is...

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John R. Cox replied on Feb. 7, 2020 @ 02:56 GMT
Eckard,

page 6 [15]

physically, if we pass the pole of a magnet past a conductor, a rise and fall of induced voltage will occur, but the direction of the induced current will not reverse bias. The rate of change of flux density in proximity to the conductor is proportional to the value of induced voltage, so it makes clear sense that only positive reals are necessary and while the sinusoidal shape of rate of change would approach a nil value of voltage tangent to either the upper or lower limits of a continuous sinus, there would exist a real positive voltage level in the same direction of potential in the conductor.

I have long thought that such a scenario as this, rather than the typical plot with a 'zero' baseline and positive and negative deflections commonly interpreted as the signature of a transverse wave; might be the realistic signature of a soliton of linearly projected electro-magnetic emission. Perhaps both Newton's corpuscle of light, as well as the wave model, are at least half correct. jrc

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H.H.J. Luediger wrote on Feb. 5, 2020 @ 16:21 GMT
Dear Eckhard Blumschein,

very much enjoyed...just one comment. "As-if" (the metaphor) and the model differ in an essential respect. The metaphor requires disparate, incommensurable or orthogonal 'moments', whereas the model builds on similarity with what it models. In other words, the metaphor augments, whereas the model explains, describes or represents. Hegel was the only one to see Kant's mistake to regard e.g. the finite and the infinite (and dialectic in general) as a logical opposition (A and not-A). For Hegel the finite and the infinite fall into different categories, namely quantity and quality. Hence they share no common measure. Since logic is founded in identity, it must fall into trap of explaining the metaphor and thus answer meaningless questions.

regards,

Heinz Luediger

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Author Eckard Blumschein replied on Feb. 6, 2020 @ 18:31 GMT
Dear Heinz Luediger,

Thank you for your comment. You are an EE as I was too,and you were perhaps not forced to deal with Hegel's dialectics while I didn't like dialectic materialism which was obligatory to me as a precondition of promotion. Didn't Heg,l say "Die Atomisten denken zu materiell"? Donn't get me wrong.I consider thesis, antithesis,and synthesis valuable. However, if I recall correctly, it was Marx who criticized "abstruse Hegelei". What about physics I would like to rather trust in Kant who wrote in Kritik der reinen Vernunft: "Die Eigenschaft von Größen, nach welcher an ihnen kein Theil der kleinstmögliche ist heißt Continuität. Raum und Zeit sind quanta continua". Notice his word Eigenschaften. Both being finite and being infinite are properties, in other words qualities, not quantities. Please read $ 2 of my essay carefully.

I didn't use the word metaphor exactly as perhaps do you. To me, a metaphor is an imaginary way of describing something by saying that it is something else which has the qualities that I am trying to describe.

Because you seem to be a prolific essay writer, I would like to ask you for any hint to some overlooked imperfection in basics of mathematics and/or physics.

Of course, I would also like you to take issuw concerning my views on the addressed in my essay positions by Fourier, Hilbert, Hausdorff, Einstein, and Feynman.



Regards

Eckard Blumschein

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H.H.J. Luediger replied on Feb. 6, 2020 @ 21:05 GMT
Dear Eckart,

I don't think we really disagree on the notion metaphor, rather we seem to look at it from different perspectives. Maybe my forthcoming essay can clear up matters a little bit...

Generally my reasoning rests on the impression that neither physics nor mathematics are monolithic (coherent) blocks of knowledge, but sets of Absolutely non-contradictory (orthogonal) theories, theorems, etc. So, everything seems to be connected by being Absolutely disconnected in quasi-space. If so, logical positivism tried to logically (the math is just heuristic) connect things which share no common measure and thus created loads of conundrums. Logical positivism is dead - long live logical positivism!

Heinz Luediger

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Author Eckard Blumschein replied on Feb. 8, 2020 @ 05:55 GMT
Heinz,

I look forward reading your essay.

Eckard Blumschein

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Author Eckard Blumschein wrote on Feb. 10, 2020 @ 04:35 GMT
Dear all,

Rethinking the question

"Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability?"

I would like to once again support T. Palmer: Back to basics!

Past and future are not undecidable from each other, except for theories that are used as putative fundament of physics.

I promised to John Cox to elaborate, and this will take me some time.

Just one detail:

Having checked my essay for decisive loopholes in my reasoning I realized that I did perhps not yet clearly enough distinguish between Fourier's undecided with respect to the choice of t=0 and therefore redundant complex transformation on one hand and Heaviside's fictitious split into an even and an odd component on the other hand. Heaviside introduced the reference t=0. Fourier or Heaviside, on which fundament should QM be based? For convenience, one may calculate as if Fourier was right.

Eckard Blumschein

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John R. Cox replied on Feb. 11, 2020 @ 15:03 GMT
Dear Eckard,

already I'm in over my head. But in browsing to get a better idea of what (and how) Fourier distributions are and 'get back to basics', I ran across this very brief and concise paper on Fourier Transforms of a Heaviside Step Function: a Tragedy.

cs.uaf.edu/-bueler/M611heaviside.pdf

and have to wonder if Bueler is demonstrating the same, or similar, problem that you identify in the operations of F & H.

It strikes me that if we take the energy signal as going to infinity, then that is really a mathematical convenience not an existential property. It simply allows an open ended process that would integrate any number of steps once a signal was switched on... that is, the duration of repeated pulsations is unknown and contingent on putting in by hand, an 'off' switch. Also, the 1/2pi term would naturally apply to the orthogonality of electromotive induction, or in a 3D+T wave model - the 90* rotation between the planes of direction of field strengths of the electrical and magnetic components of an EM signal. best jrc

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Author Eckard Blumschein replied on Feb. 12, 2020 @ 01:36 GMT
Dear John, dear all,

"Fourier Transforms of a Heaviside Step Function: a Tragedy" ??

I prefer using the word tragedy to human lives. Just a few excamples:

Archimedes was killed: Don't disturb my circles

Matrin Luther saved Stifel who had calculated and predicted the immediate doomsday

Georg Cantor got insane, claimed having got the CH directly from God, and died in a madhouse

Kronecker was mobbed and died

Ritz and also Minkowski got suddenly ill and died

Suicides by Boltzmann, Hausdorff, Turing

Gödel's paranoia

Grothendieck's disappearance

In the case addressed by Buehler, there is a quite simple logical solution - admittedly one has to get free from traditional formalism but go back to basics as I tried to indicate in § 2 of my essay.

My style of teaching is a bit different from Feynman's. I hope, you may find the solution yourself soon. I will give you just a hint. Feyman allegedly refused to explain half spin. Why didn't he just mention that a full circle (360°) of cos equals to 720° of cos squared?

Once again, the solution is easily to find out for anybody with readiness to critical tinking. Don't shy back from questioning a very basis of mathematics. Admittedly I was inspired by a Professor Schwarz of South Africa whom I met in Milano in 1992, Dean Mückenheim provided me with many details, and I recall having read a lot of literature in German, e.g. Hans Gericke and Oskar Becker.

Best,

Eckard

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Author Eckard Blumschein replied on Feb. 13, 2020 @ 19:07 GMT
We should not neglect what John addressed: My suggestion “calculate as if there was no causality but be careful” does also relate to the artificial boundaries of the interval under consideration.

However, I claimed having a simple logical solution to the Fourier transform of the Heaviside function. Here it is:

H(t) can be split into two fictitious parts, the even one = ½ and the odd one = ½ sign(t).

Notice: Frequency analysis of measured (i.e. past) data requires H(-t) and sign(-t).

With cos(t) + i sin(t) as kernel of Fourier transform, integration from minus infinity to plus infinity yields the real part of H() = ½ and the imaginary part = 1/i

Bueler’s example doesn’t share the widespread mistake to define H(t) with t>=0 instead of t>0, and it illustrates that calculating as if setting t=0 in H(t) was correct may lead to wrong results. Use of distributions is not easy and perhaps unnecessary.

Notice: Euclid's ideal point, something that has no parts, contradicts to a notion of number which is, as illustrated by Hausdorff, rather based on embedded dots.

By the way, Heaviside hated geometrical evidences. Gauss criticized the desire for unnecessary acuity. Why? A point “at zero” cannot be split into a positive and a negative part. The only solutions are to calculate as if or to have a 0+ and a 0-. According to Salviati the relations larger than or smaller than are invalid for indefinitely large (as well as small) numbers. We may add: They are invalid for any truly real numbers, not only for infinity and zero.

is

Anyway, if there is no natural reference as with the t=0 of H(t) but not with Fourier, an arbitrary choice is unavoidable.

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Jonathan J. Dickau wrote on Feb. 14, 2020 @ 15:30 GMT
Thanks for your comments on my page Eckard...

This essay looks very interesting, judging by the abstract, and I shall look forward to reading it. For the record; Hilbert was not alone, and many people have put faith in the 'excluded middle' when in fact there was a middle ground, spawning what I call 'false dilemmas,' and much confusion of course.

More later,

Jonathan

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H.H.J. Luediger wrote on Feb. 16, 2020 @ 12:54 GMT
Dear Eckart,

the more I read your essay and follow the discussion, the less I see the point you're going to make. Fourier states in J.B.J. Fourier, Theorie de la chaleur dans les solides, 1807:

The integrals we have obtained are not only general expressions that satisfy the differential equations; they represent in a different way the natural effect, which is the object of the problem. This is the main condition that we have always had in view, and without which the results of the operations would appear useless transformations. [note the terms 'differential equations' and 'natural effect']

What he says is, that mathematics is a desert with few oases called physics. My personal guess is that less than one percent of the totality of known math has correspondence in the 'world'. And this tiny part must be used - not questioned, for there is no ever knowable connection between these bits of math and the PHENOMENA.

Best regards,

Heinz

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Author Eckard Blumschein replied on Feb. 17, 2020 @ 04:37 GMT
Dear Heinz,

Of course, we may follow not just Fourier and calculate as if there was no causality. Having quoted from page 7 of the English translation of Fourier’s 1822 theory: “… mathematical analysis is as extensive as nature itself, it defines all perceptible relations, measures times, spaces, ...” I maintain my objection: Fourier was wrong in this decisive respect. My argument is quite compelling: Measured data which are available for mathematical analysis do definitely not extend from minus infinity to plus infinity but they only include the past. In other words Fourier was wrong because he uncritically adopted a widespread fatalistic philosophy that generalized too much (cf. the word general expressions in what you quoted).

Did this better explain my point?

Best regards, Eckard

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H.H.J. Luediger replied on Feb. 17, 2020 @ 10:47 GMT
Dear Eckart,

Fourier was a pre-modern, a man of classical physics, that's why I highlighted 'differential equations'. TIME to him was something totally different than for historians and logicians, i.e. the romantics. If my sources are correct, he wrote the variables on both sides of the FT as 'x' and 'u' (which are still used in Fourier-optics), not as 't' and 'f or omega'. So, we disagree on the concept of TIME with no chance of reconciliation. Nevertheless, good luck for the contest!

best regards,

Heinz

P.S. Hegel abhorred of FICHTE'S Dreischritt of thesis-antithesis-synthesis, because for him dialects is not a process set in grammatical-logical-historical time but a principle of the mind. That's why for him 'evolution occurs at a single stroke'.

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Author Eckard Blumschein replied on Feb. 17, 2020 @ 18:00 GMT
Dear Heinz,

At the time of Lagrange, Laplace, and Fourier, differential equations were not new, and heat conduction is not thinkable without time. Admittedly, I don't understand why you are not in position to accept compelling arguments and at least correctly write my name Eckard (neither Eckhard nor Eckart). Why do you disagree with my concept of time? I wonder if there is to engineers an acceptable alternative to time as something that includes past and future in common sense.

Even if I am just a bit familiar with Fourier acoustics and not at all with Fourier optics, I am aware of wave numbers k, evanescent modes etc. Complex spatial frequencies correspond to ordinary complex frequencies as elapsed time corresponds to the likewise always positive quantity radius r, not to spatial coordinates x, y, z.

Best regards,

Eckard

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Robert H McEachern wrote on Feb. 18, 2020 @ 18:13 GMT
Eckard,

I enjoyed your essay.

A few comments:

"There is a decisive advantage of digital over analog technology: Digital signals may cope with the noise-caused loss of decidability." Any actual advantage comes from choosing to "represent" only discrete symbols, like the letters of an alphabet, rather than from merely representing an analog signal via digitized samples taken...

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Author Eckard Blumschein replied on Feb. 20, 2020 @ 16:25 GMT
Dear Rob,

As I expected, your comments largely confirm my essay.

In particular I hope our different approaches may eventually agree on consequences concerning QM. You didn’t quote my complete sentence. I wrote:

“Unfortunately, one cannot even prove the theory of quantum mechanics wrong, because it was not logically derived but just heuristically fabricated by...

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Robert H McEachern replied on Feb. 20, 2020 @ 17:48 GMT
Eckard,

Much of what Schrödinger and Heisenberg did, was "logically derived"; the problem is, some of the axioms their derivations were founded upon (such as perfectly identical particles, and using a single Fourier transform (wavefunction) to describe multiple particles) are demonstrably invalid, in any realistic rather than idealistic (noise-free) conception of reality,...

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Author Eckard Blumschein replied on Feb. 21, 2020 @ 05:13 GMT
Robert,

As to evade useless quarreling with a believer of complex FT on whether or not truncation (FIR) in combination with shift rescues FT, I would like mocking: May we attribute to the complex wave function a behavior similar to phase deafness in case of hearing, instead of the mysterious so called collapse of wave function?

Eckard

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Author Eckard Blumschein wrote on Feb. 21, 2020 @ 14:06 GMT
On p. 2 of Robert McEachern's 2015 essay I found the expression "Fourier Uncertainty Principle" which was certainly meant in the sense of Heisenberg's Uncertainty relation. Let me reiterate, Fourier was wrong when he believed that the complex transformation he advertised is as extended as is nature itself.

It is undoubtedly often advantageous to calculate as if this was the case. However, be careful ...

Eckard Blumschein

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John R. Cox replied on Feb. 23, 2020 @ 15:27 GMT
Eckard,

that states it quite simply, and nature is not likely to be adequately described by any one particular method of analysis. Let me again commend you on the effort you have put into writing and conversing in the casual idioms of the English language. You must have labored long on your essay, and it does read well for those of us whom have not had to learn any other language. Thanks again, this has been a learning experience for me, and good luck with the judging. best - jrc

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Author Eckard Blumschein replied on Feb. 27, 2020 @ 05:38 GMT
John,

“… nature is not likely to be adequately described by any one particular method of analysis.” ???

A Polack wrote: “The map is not the territory.” In so far I partially agree. The mathematical map in terms of abstracted laws extends from minus infinity to plus infinity. Nature is the unchangeable territory. It does not yet include what is still open to influences in the merely more or less predictable future. Fourier got utterly popular by providing something that is very elegant one the abstract level of theory but contradicts to common sense: Complex analysis seems to allow a spectral analysis not just of data from the past but also of not yet available future data. Consequently complex analysis implies to deny the distinction between past and future as actually did Einstein and Hilbert. Well, within a model or a record there is no “now”: The map as well as a photo are not the territory.

I already mentioned that science doesn’t require a beginning of time (point of creation), and I add we don’t need an end of time (doomsday) either. However, engineers like me need the here and the now.

Kind regards,

Eckard

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