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RECENT POSTS IN THIS TOPIC

Eckard Blumschein: on 5/17/20 at 4:26am UTC, wrote “Calculate as if there was no causality … but ” implies what I wrote...

Jonathan Dickau: on 5/15/20 at 12:31pm UTC, wrote Wow that's quite informative... I think many people fail to grasp what the...

Eckard Blumschein: on 5/15/20 at 5:44am UTC, wrote Dear Jonathan Dickau, Thank you very much for your encouraging comment. I...

Jonathan Dickau: on 5/13/20 at 2:16am UTC, wrote And I want to add... I like that you mention the distinction between thumb...

Jonathan Dickau: on 5/12/20 at 16:28pm UTC, wrote I should amend that. I said it incorrectly. People make 'limiting or...

Jonathan Dickau: on 5/12/20 at 16:25pm UTC, wrote This essay is excellent Eckard... Your deep analysis displays an...

Eckard Blumschein: on 5/2/20 at 3:39am UTC, wrote Dear Hippolyte, Let me try to clarify in what context I am claiming to be...

Hippolyte Dourdent: on 5/1/20 at 0:11am UTC, wrote Dear Eckard, I finally had the time to read your essay, that I found...


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FQXi FORUM
July 11, 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.

Download Essay PDF File
Note: This Essay PDF was replaced on 2020-03-24 03:57:51 UTC.

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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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Author Eckard Blumschein wrote on Mar. 2, 2020 @ 05:53 GMT
While perhaps nobody may deny that the complex Fourier transform introduces an arbitrary reference point, You Tube is propagating a video: “But what is the Fourier Transform? A visual introduction”.

The video repeatedly nicely illustrates how an endless sinusoidal function of time can be wrapped around a circle. Is there a problem? Yes: One may calculate as if there was no causality but in reality the past is closed and the future is open. Accordingly there is a border between past and future that can be shifted at will on the level of abstract models but definitely not at the basic level of physical reality.

Fourier’s theory as well as the video neglects something that is also quite plausible: An endless path is (only) imaginable along any closed loop, no matter whether it forms a circle or an interval between two mirrors. In the latter case, a standing wave obeys Neumann or Dirichlet boundary conditions at the surfaces of the mirrors.

Endlessness at both sides implicates the need to chose a point of reference at will.

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John C Hodge wrote on Mar. 2, 2020 @ 18:49 GMT
Eckard:

I read your essay with great interest. You'll see mine has some common ground. However, I understand your view is the characteristics you mention may be used by physics but with caution to relate to observation (not sure you meant the "observation" part). Could you accept the idea that the use of the math characteristics produces problematical physics and should be indicate a model that needs a redo (my thesis)?

One thing I treat lightly (lack of space) was the place of error analysis/statistics in misleading and inadequate for physical models. This point was explored in Nielsen, Guffanti & Sarkar arxiv:1506.01354 "Marginal evidence for cosmic acceleration from Type Ia supernovae". This point was further explored in Sabine Hossenfelder's recent interview of S. Sarkar https://www.youtube.com/watch?v=B1mwYxkhMe8&list=PLwgQsqtH9H
5fe4B5YCF3vcZgIkMMULS7z

Let me add a bit on a previous comment on you essay, The truncated Fourier analysis results in the next term after truncation is the Uncertainty (Heisenberg's Uncertainty?).

Would you comment on the idea that all the added dimensions, imaginary numbers, and things like Fourier constants do not improve Understanding or physics. They merely mask better physics.

A bit on numbers. As you see, I hold only cardinal numbers as useful with irrational and transcendental function as contributing to the error between observation and math. I understand the natural number's interest is describing an extension of a point to a line to want to include such numbers. But I reject imaginary numbers as being an unnecessary crutch.

I also note the Turing's proof includes the ordinal number's which makes the proof nonphysical. Similar nonphysical comments are in Godel. I wish I spent a bit more space on this point - but space.

Hodge

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Author Eckard Blumschein replied on Mar. 3, 2020 @ 16:50 GMT
JC Hodge,

My main credo/topic is causality. You wrote: “greater Understanding and greater Wisdom yields survival and population growth.” Are you sure that survival and unlimited population growth don’t eventually exclude each other? This perhaps shocking question of mine intends to make aware of the importance and the risks of idealization in general, including physics. Be careful, the map is not the territory. Nonetheless, I suggest continuing to deliberately calculate to some extent as if there was no causality.

By the way, Heisenberg’s uncertainty is not bound to complex Fourier transform. It relates to conjugate pairs like time and frequency with real-valued cosine transform too.

Eckard

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John C Hodge replied on Mar. 3, 2020 @ 21:52 GMT
Eckard

Note the "and" implying both. Certainly Malthus identified a rule of nature. Technology has allowed a greater population level. But Malthus was correct, population does increase faster than even technology. So, either humanity deals with Malthus' nature or nature will do the population limiting itself. Humanity is a "keystone" species (Serengiti Rules") which means starvation is nature's way of dealing with us. Such has been the case throughout history. The nature's contraction comes at the end of a warm period where food production allows the overpopulation. Then a cool period restricts food production to levels below that required by the population. Civilization collapse follows. So, now we are facing a coming cool period. Has humanity's morals going to prevent a collapse of civilization? I think not. The moral of supporting the weak and non-producers may guarantee collapse. Note the Polynesians on isolated islands had to deal with the food limit by supporting infanticide (of the weak) and suicide.

Like your "territory analogy. Certainly, The line (math) on a map (transformation) is not the road (physics).

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Author Eckard Blumschein replied on Mar. 4, 2020 @ 09:12 GMT
John C Hodge,

My message is: Be careful if calculating as if an ideal map was the territory even if it is of course different. In case of ethics, the biblical ideal is to get more power by getting more followers. As far as I now, Malthus did not yet vote for a more comprehensively responsible ethics because he focused on nutrition and ignored that the main risk is not directly malnutrition but side effects of more efficient methods to exhaust and irreversibly poison nature.

At first, I suggest dealing with the ideals in mathematics and in physics. Is my distinction between Euclid’s ideal point and mathematician’s dot plausible to you? Wilhelm Busch was mocking:

Who cannot imagine a point is simply too lazy for that. (My source: Mückenheim “Die Geschichte des Unendlichen”).

Eckard

.

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Author Eckard Blumschein wrote on Mar. 3, 2020 @ 19:33 GMT
Tim Palmer called some questions of mine „deep questions!! “. I guess, typical mistakes in mathematics cannot at all be so deeply rooted that they cannot be clearly addressed, and most likely it is often possible to find out what went wrong in history.

My reason to delve into the fundamentals of mathematics was the rejection of my suggestion to allow R+ and cosine transform instead of R. My argument was: In order to describe the past (or the future) alone, on does not need time values that extend from minus infinity to plus infinity. In particular, data that are not yet available cannot be analyzed. I am arguing that R+ and cosine transform CT as a special cases of R and FT relate to FT as does N to Z. R and FT only differ from R+ and CT in that they need an arbitrarily chosen reference point. Instead of accepting R+ and CT, some mathematicians denied the possibility to separate R+ from R. Indeed, modern topology doesn’t allow a discrete cut. I blame Hausdorff and Dirac for making this mistake very obvious. I found out, as I indicated in my essay, that the notion of continuity as used by Rolle is inappropriate in case of a discrete jump. By the way Rolle understood in contrast to Descartes that -1 is larger than -2.

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Author Eckard Blumschein wrote on Mar. 4, 2020 @ 17:38 GMT
Hopefully I could find out why the notion infinity has a record of causing confusion. Just a few examples: Bernhard Bolzano (1781-1848) who created the notion Menge (= set) wrote “Die Paradoxien des Unendlichen” Reclam Leipzig 1851

Cantor: On the different points of view with respect to the actual infinity (in German) Halle 1890

Hilbert’s hotel is famous, also his paper “Über das Unendliche” in Math. Annalen 95(1925)165

Lavine „Understanding the infinite“.

I see the latter inappropriate to someone who tries to benefit from “understanding”.

I am already not sure whether to criticize Wolfram’s definition of infinity as “an unbounded quantity that is greater than every real number or just smile because the real numbers are conceptualized as endless. To me, the property of being infinite (= unbounded = endless) is an absolute quality, not a quantity.

Relative endlessness means something very useful while logically quite contradictory. Being endless with respect to something as introduced by Bernoulli and Leibniz tamed the nonmathematical quality, made it a usable quantity as if it still was a quality.

There are consequences: Singularity functions like e.g. sign(x) do strictly speaking not fit into what I am calling a mathematics of continuity (anything flows) or with other words Rolle’s mean value postulate.

Accordingly, the definition sign(0)=0 is unfounded, etc.

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Author Eckard Blumschein wrote on Mar. 5, 2020 @ 15:37 GMT
While Laurent Schwartz felt guided by his desire to be rigorous and logical, his basic idea effectively was just the opposite: Abandoning Euclid’s indivisibility of a point for the sake of the analogy with electrical dipoles, quadrupoles, and so on.

The theory of distributions followed Rolle when introducing so called testfunctions D, i.e., smooth functions which have compact support.

Already the notations and conventions were “correcting” plausible mathematics:

N0:={0}∪N

⊆ means subset, ⊂ will not be used

Etc.

What about claimed applications cf. “Some applications of the theory of distributions” Lectures on Modern Mathematics, vol. I, New York: Wiley, 1963, p. 23-58

Seen from the perspective of engineers and physicists, the intriguing possibility of endless repetition of the operation differentiation is rather an unnecessary and distracting support of e.g. Hausdorff.

Well, one may calculate to some extent within the theory of distributions and adopt Dirac impulses. However, be cautious and don’t ignore arguments against unjustified consequences of belonging topology. If singularities are justified at all, then certainly not inside smooth functions. Don’t get me wrong, I am a fan of ideal (not smooth) singularity functions like ramp, step, pulse and doublet. See my earlier essays.

Point charges, line currents and the like are ideals that should not be extended by force to inappropriate models. It is just often best to calculate as if a dot was a point, provided one understands what one does.

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Author Eckard Blumschein wrote on Mar. 6, 2020 @ 04:29 GMT
If you pretend to calculate as if you were blindly following a pied piper who attracts crusaders (nowadays by means of seemingly compelling videos) then be careful: You need not giving rise in public for getting burned as was Giordano Bruno. You are not obliged to become one more crank among thousand who failed to find and point out what actually went wrong with putatively compelling mathematical evidence.

For instance, G. Cantor’s transfinite numbers seem to contradict common sense. Their defenders called them counterintuitive as if common sense was inappropriate. Actually, it was Cantor who was led by his naïve intuition: “einfaches Hinüberzählen, mehr als unendlich viele Zahlen”. The distinction between Cantor’s aleph zero and aleph one is plausible to me. Anything else including the diagonal arguments should be judged from the perspective of the (so far missing) application in science. While a critical study of Fraenkel’s 1923 textbook reveals the cardinal logical mistake, the deeper reason for the acceptance of the rather strange transfinite set theory may be found in a desire of mainstream mathematicians to cope with inconsistencies affecting the notion number: Are they anything one may calculate with? Is this a good question? The natural numbers combine an idealization (the number one) with equality based repetition (addition). In this sense, mathematics is based on logics but not Hilbert’s other way round.

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Author Eckard Blumschein wrote on Mar. 6, 2020 @ 18:03 GMT
At Quora, Cristinel Stoica recently reminded of his FQXi essay 1357. So far I didn't find a current essay by him. May I hope for himself or someone else taking issue concerning what I am calling mistakes?

Eckard Blumschein

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John C Hodge wrote on Mar. 7, 2020 @ 13:18 GMT
Reply to Eckard Blumschein's comments:

Could you accept the idea that the use of the math characteristics produces problematical physics and should be indicate a model that needs a redo (my thesis)?

One thing I treat lightly (lack of space) was the place of error analysis/statistics in misleading and inadequate for physical models. This point was explored in Nielsen, Guffanti &...

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Author Eckard Blumschein replied on Mar. 8, 2020 @ 00:23 GMT
Dear John Hodge,

I appreciate the opportunity you gave me to hopefully better explain what I meant with "calculate as if the model was identical with the basic reality behind it".

While I agree: "Singularities or infinities are not physical", I don't see them "indicative of incorrect calculation" but rather of careless assumptions and/or interpretations.

I don't at all reject imaginary numbers as being unnecessary.

Is "the distinction between a dot and a point is that there is no distinction"? Well, I blame the mathematicians for ignoring Euclid's indivisible point. They are instead operating with something for which I don’t have a better denotation in English language than the word dot. Words like dot-set topology theory and dot-charge sound strange. They make aware of denied mistakes. Also, we should strictly speaking distinguish between absolute endlessness and the admittedly very reasonable relative infinity.

Again: Calculate as if but be careful.

Carefulness demands too that I will explain to you later in what I see you wrong.

Best,

Eckard



Best,

Eckard

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John C Hodge replied on Mar. 8, 2020 @ 13:40 GMT
Wonderful. I appreciate you comments where you suggest I'm wrong. It would certainly help the development of my STOE. I would appreciate you views if they are supported by observations/experiments and not be rejected by observations/experiments.

You may also note that messages may be sent to my RG page where the many papers of the STOE are displayed.

Hodge

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Author Eckard Blumschein replied on Mar. 8, 2020 @ 21:39 GMT
Stay calm, John Hodge,

I did not yet at all deal with your STOE, and I see you my ally concerning birth control.

Nonetheless I will today begin with evidence against your opinion that "the idea of conjugate pairs is an artifact of assuming particles are infinite waves."

In Fig. 1 of my third FQXi essay I showed frequency vs. elapsed time plots which were calculated by means of COSINE transformation, not the complex-valued Fourier transfotm. The f vs.t hyperbolas exhibit the same uncertainty relation as found by Heisenberg for P vs. q/h. Notice, Planck's constant is just required as to get an dimension-less argument. Other conjugate pairs are omega and t as well as k and r.

Can you provide a source for your wrong claim or is it your own guess?

Eckard

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John-Erik Persson wrote on Mar. 11, 2020 @ 19:47 GMT
Eckard

I am impressed by your theoretical knowledge. So, i have much to learn from the article. It is a very broad article.

Thank you for writing on my page also.

Since you mention Euclid I havre question for you (if you are interested you can answer on my page):

Is it correct to define parallellism by a point that does not exist?

With best regards from _________________ John-Erik

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Author Eckard Blumschein replied on Mar. 12, 2020 @ 04:57 GMT
John-Erik,

First of all, I have to apologize for an embarrassing typo in my essay: Factionalism should read fictionalism.

I gave a link to David Joyce from whom I got my admittedly very limited knowledge of Euclid’s Elements.

The question you are alluding to is more directly addressed for instance in https://www.jstor.org/stable/2973238?seq=1#page_scan_tab_con
tents

I dislike unnecessary academic disputes concerning mathematical existence, Platonism, finitism, etc.

Instead I suggest calculating with careful critical interpretation as if our models and laws (maps) were the nature (the conjectured real territories). Accordingly:

- Nature doesn’t model (calculate) itself.

- Bolzano was wrong when he meant that a line of doubled length contains twice as many points.

- Common sense tells us that Euclid’s points are something ideal, quite different from dots.

- Experience tells us that one must not deny causality even if this is not obvious in laws of nature.

- Being infinite is also just an ideal feature. Singularities and closed loops are unphysical.

Eckard

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John-Erik Persson replied on Mar. 13, 2020 @ 15:00 GMT
Eckard

I asked you:

Is it correct to define parallelism by a point that does not exist?

The link you gave did not work.

With regards ____________ John-Erik

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Author Eckard Blumschein replied on Mar. 13, 2020 @ 18:18 GMT
John-Eric,

I immediately found

https://mathcs.clarku.edu/~djoyce/java/elements/element
s.html

This link is still listed on second place at wikipedia among "other external links". Because I didn't have contact to David Joyce for years, I can only hope he is well.

What about the "existence" of the fictitious point at infinity, we should agree on that there are no tangible points and lines at all in reality. One may only calculate as if e.g. there were point charges, line currents, and other singularities.

Albert von Sachsen (1316-1390) was close to this insight when he wrote: a Wooden bar of infinite length has exactly to many points as the whole 3d space.

Eckard

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Flavio Del Santo wrote on Mar. 16, 2020 @ 21:08 GMT
Dear Eckard (if I may),

thank you for a well-argued essay, there is so much food for thought here!

It seems we have so many ideas in common, at least regarding the different uses of mathematical languages in physics. I would be thankful if you could take a moment to have a look at my essay, where I argue, among other things, that one could envision an indeterministic physics by rejecting the infinite precision of real numbers (a program of research that I carry out with Nicolas Gisin).

More of a small historical precisation, the beginning of your essay states the common attribution of "shut up and calculate to Feynman", which however, seems not to be the case. David mermin has an eccellent story on this: https://physicstoday.scitation.org/doi/10.1063/1.1768652

Anyw
ays, good job, very high rate from my side!

Best wishes,

Flavio

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Author Eckard Blumschein replied on Mar. 17, 2020 @ 01:37 GMT
Dear Flavio,

I am not amused by David Merlin's joke:

"Theoretical physics is done by physicists who lack the necessary skills to do real experiments; mathematical physics is done by mathematicians who lack the necessary skills to do real mathematics"

It reminds me of similar ones:

Extraordinary professors are unable to do something ordinary: Ordinary professors are unable to do something extraordinary.

Your rejection of the infinite precision of real numbers seems also to be an old hut. Already Gauss criticized striving for numerical exactness.

What about your essay, I confess being a fan of Popper's opinion too: The future is open, and I also agree with Shannon: The past is closed. I will read your essay and comment on it.

Did you already comment on Alan Kadin's prediction that quantum computing will for two reasons not work as envisioned? I would like to appreciate his courage. Perhaps, his essay "Just too many people" is at least as unwelcome as obviously also is Euclid's definition of a point to John-Erik Persson and to followers of Cantor's, Hilbert's, and Hausdorff's finitism.

Good luck,

Eckard

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Author Eckard Blumschein wrote on Mar. 24, 2020 @ 03:57 GMT
Eckard Blumschein re-uploaded the file Blumschein_As_if.pdf for the essay entitled "Calculate “as if “… but be careful" on 2020-03-24 03:57:51 UTC.

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Peter Jackson wrote on Mar. 24, 2020 @ 18:09 GMT
Dear Eckard,

Wonderful job! You excelled yourself this year Eckard, not only in your message and argument but in arrangement and English language clarity.

I rarely read essays twice but did yours (I often first diagonally 'speed read') as in many ways it's as pertinent and concentrated as mine. I did find and agree your added word! I also learned a few new viewpoints, i.e. Weyl's quote on 'quantum laws'; "no acceptable solution is in sight".

Agreeing a thesis helps of course, and ours are very close, but you also did well in all scoring criteria. A few specific comments and questions;

1. We fully agree on the excluded middle (which I greatly expand on).

2. I like Leibniz' 'Metaphysical lower level' & symmetry with what I discuss.

3. Do not asymmetric twin and elliptical spiral or helical paths better model reality so provide greater 'appeal'?

4. I like your bravery challenging Fourier, but validly. However consider a helix with a central axis 'line'. Viewed from any side we have a sine curve with the axis as 0 and +1 top and -1 the bottom. A twin helix is the Dirac equations sine/cos curve. Is not the result of simply rotating the observer 90 degrees also interesting?!

5. I agree Feynmanns flawed mantra was 'Shut up...' but in researching their works indeed found it first written by Mermin. (Feynman adopted it & wrote complimenting a Mermin paper).

6. Your p.8 QM comments seem fair, but resolved if corrected by replacing 'quantum spin' with Maxwell/Poincare's SECOND momentum case on rotating spheres (inversely changing linear equatorial and polar rotation). Surely just reproducing QM data classically must be adequate to show QM's illogicality 'wrong'!? It the problem not just overcoming 'beliefs'?

Anyway, very well done. I think you'll like mine too. (but also may need to read it a slower 2nd time!)

Very best

Peter

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Author Eckard Blumschein replied on Mar. 27, 2020 @ 06:00 GMT
Dear Peter,

I used my chance to replace my submitted essay as to correct the typo "fact..." instead of "fict..." and to delete the link to David Joyce's excellent but unfortunately outdated address. My hint to Euclid's Elements should be sufficient.

Of course, Euclid's definition of a point as something that has no parts is unwelcome to modern mathematics which has pragmatically arranged not just with Leibniz' relative (strictly speaking finite, not transfinite) notion of infinity but also with belonging modern axioms including ZFC.

No parts means beyond endless divisibility. Preference to operating with numbers fundamentally contradicts to the Greek logics up to Salviati.

Thank you for correcting me: David Mermin confessed it was he, not Feynman who coined the advice "shut up and calculate".

This does not change my suggestion: Calculate as if modern math was logically consistent and did matter but be careful: Already Spinoza meant: "It is not less nonsensical to claim that ... the body is composed of areas, areas of lines, and lines of points". While I understand point set theory as dot set theory, I am still looking for a word that distinguishes the ideal line from the infinitesimal thin one.

Do you too agree with Bee on her rejection of impossibility-laws as fundamentals even if the topic asked for that?

How do you judge Alan Kadin's prediction?

Very best,

Eckard

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Author Eckard Blumschein replied on Mar. 27, 2020 @ 09:22 GMT
Having found in my dictionary the translation of the German word Kondensstreifen: condensation trail, I hope this may dispel Peter's distrust.

I consider the distinction between past and future and the distinction between reality and ideal model essential but not a reason not to calculate as if Cantor, Feynman and Mermin were correct.

More later at Peter's thread.

Eckard

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Peter Jackson replied on Mar. 28, 2020 @ 13:30 GMT
Eckard, I agree ref Cantor etc. Also ref planes condensation or 'con trail' as a good example of how motion forms shear planes form vortices of condensed matter (water vapour in this case) from a condensate. I simply invoke a smaller gauge of the same process to condense fermion pairs ("matter") from the "Higgs Condensate" as Kalusa-K etc. all higher order 'dimensions' and dark energy. That simple 'phase transition' model shows massive (lol) resolving power.

As nature (as a opposed to geometry) is entirely non-linear I'm not so concerned about 'line' semantics. In free media I'm familiar with 'direction', 'boundary', 'heading' and 'bearing' but all relate to some datum.

No, I don't agree Bee's dismissal, though she was also uncertain! But they all fall on the 'metaphysics' side of the divide so nature may ignore them! i.e. a cyclic universe is consistent and also won't 'halt'.

I agree with most all in Alan Kadins essay, but see my comments there. I think far better understanding is perfectly possible but we're still to dimwitted and reliant on embedded old nonsense beliefs! My 2010-11 essay "2020 Vision" anticipated intellectual evolution may escape that by now. Hmmm. But I'm always the optimist!

I look forward to your thoughts on mine.

Very best Peter

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basudeba mishra wrote on Mar. 30, 2020 @ 16:58 GMT
Dear Sir,

Feynman’s advice: “you cannot at all understand quantum mechanics” is correct to a limited extent because of the limitations to our capabilities. But it ignores the fact that if everything is made up of the same fundamental particles, they must follow the same set of physics. This was in the back of his mind, when he added: “shut up and calculate!” This is not because...

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Author Eckard Blumschein replied on Apr. 10, 2020 @ 01:41 GMT
Dear Basudeba Mishra,

I was not aware that a Mogul (not a mogul) was a Muslim ruler in India in the sixteenth to eighteens centuries. It is a pity that very old Indian wisdom didn't get known in Europe, e.g.: “You can’t take one part of a fowl and cook it, yet expect the other part to lay eggs.”

You criticized my idea of reality as the “logical negation of merely abstract ideas” while you consider it “knowable and describable in any language”. Of course we agree: A street is not a line, however, I am not a seeker for truth but merely a seeker for mistakes. Isn’t it possible that you may realize that calculating with imaginary numbers is a very successful reality?

Respectfully,

Eckard Blumschein

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Edwin Eugene Klingman wrote on Apr. 4, 2020 @ 05:21 GMT
Dear Eckard,

I am happy to see that your essay has stirred great interest, as I thought it would.

This is simply to tell you that my essay is now online, and invite you to read it:

Deciding on the nature of time and space

My best regards,

Edwin Eugene Klingman

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John David Crowell wrote on Apr. 11, 2020 @ 16:14 GMT
Eckard. Excellent essay. I learned a lot that I can apply to my work. Also, this may be of interest to you. I recently put in an “adjustment to my original essay in which I emphasized the introduction of a new fundamental level. The new fundamentals apply to physics (all sciences), math, philosophy and religion. The new level leads to the origination of a new creation process that produces “all of the order in existence” So math, physics, etc. are all results of the same creation process. What I have found is that when you go back to this lower fundamental level, you eliminate some of the humanly imposed “foundational problems” of the math, physics, philosophy, etc.. You also unify them in one theory. In the unification, you can keep the components in each discipline that work and use the new processing/results in problem areas, hard to calculate areas and areas where you are trying to unify different disciplines. Kind of like adding relativity theories to classical physics. I would appreciate your comments. John D Crowell. Note: I believe the C*s to SSCU transformation described in the appendix to my essay can be regarded as the “excluded middle” between zero and one AND between yes and no. In Successful Self Creation it is the distance between success and failure.

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Author Eckard Blumschein replied on Apr. 13, 2020 @ 11:24 GMT
John,

Did you carefully read my essay? I don’t try to unify quantum mechanics and Relativity, and I didn’t even mention creation. I carefully selected references although my main messages should be easily understandable to everybody:

- I am strictly distinguishing between the fictitious world of ideal mental constructs (including mathematical models) and the conjectured tangible world that we are calling reality.

- While not just Einstein denied the causally called distinction between past causes and future effects, I trust in the exclusion of an extended middle state (present) between them in reality.

- I showed that complex Fourier transformation must strictly speaking not be thought to be correctly based for description of real past and real future at a time. Time shift according to FT is only possible in the fictitious world of mental constructs.

Any support of these messages is welcome.

Eckard

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Edwin Eugene Klingman wrote on Apr. 27, 2020 @ 00:11 GMT
Dear Eckard,

Not sure that I answered you but I absolutely agree with Alan about quantum computing, and have believed such for years. I never bring it up since people get upset when you smash their dreams and fantasies and I did not see how that would advance what ever point I was trying to make. I’m quite certain that quantum computing will go exactly nowhere, nevertheless lots of papers will be published and lots of money will be paid.

New information from Wolfram became available 14 April, and I have updated my essay (last 3 pages) to reflect on its significance for comments that I had made to others on 9, 12, 13 April.

I think you may find it interesting; I hope so. It deals with “the fictitious world of ideal mental constructs” and potential knowledge of ontology (‘reality’). Another commenter claimed it is hubris to claim any knowledge of ontology. John Schultz’s essay suggests that non-algorithmic patterns do not impose the limitations on knowledge that algorithmic patterns profess to provide. I think that is relevant to the model I describe.

Hope you are well and stay well.

Edwin Eugene Klingman

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Hippolyte Dourdent wrote on May. 1, 2020 @ 00:11 GMT
Dear Eckard,

I finally had the time to read your essay, that I found really "thought feeding".

I think that my Gödelian hunch and your encouragement for "being careful" to not idealize nor put on a pedestal mental mathematical constructions are quite compatible. This might be why you suggested (in your comment of my essay) that your analysis of Fourier was another "hint of contextuality". However, even if I understand that your argument relies on pointing at a hidden redundancy (and thus maybe a kind of self-referential structure ?), I still struggle to see the link with "contextuality" itself (as a logical obstruction of locally consistent data) ?

Another point : Are you familiar with the topic of "quantum causality" ? (cf. e.g. doi.org/10.1038/ncomms2076 ) . Your invitation to "calculate as if there was no causality" might be appropriate to analyze these "indefinite causal orders" ("correlations with no causal order").

Best regards,

Hippolyte

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Author Eckard Blumschein replied on May. 2, 2020 @ 03:39 GMT
Dear Hippolyte,

Let me try to clarify in what context I am claiming to be careful concerning causality and QM: A basic and perhaps irrefutable argument of mine is that there is only one non-arbitrary reference to real (ontological) time. I nonetheless suggest calculating as if the reference point of time may always be chosen at will as cosi fan tutte.

Does any essay in this contest offer something with more claimed practical relevance than the prediction uttered by Kadin and supported by Klingman and McEachern? Don’t get me wrong: I am unable to read the 50 references given in Bruckner’s “Quantum correlations with no causal order“. So I feel not in position to judge whether or not he and you are correct.

The tiles of all referenced papers seem to indicate that they altogether ignored the logical justification of what Einstein denied as the now, the objective actual border between pre and after. Isn’t QM all about PREdiction?

From QuantumPhysicsLady.org I quote: “The key to understanding spin is to realize that, whatever it “really” is, its physical manifestation is the magnetic field around the particle.”

Well, both Heisenberg/Born and Schrödinger followed Fourier who confused any chosen reference point with the objective one. As a corollary: Calculate as if we all were correct but be careful. The journal nature.com is definitely something else than nature.

Incidentally, I would like to distinguish between the “frozen” causal structure of the past and the open in the sense of not yet finally structured future.

Best regards,

Eckard

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Jonathan J. Dickau wrote on May. 12, 2020 @ 16:25 GMT
This essay is excellent Eckard...

Your deep analysis displays an appreciation for the historical evolution of our ideas on the basis for logic and number that I have not seen elsewhere. Most just accept the current determination of truth values as a de facto condition, while you have shown all the subtle steps (or some of them) so we your readers can examine them anew. This is useful territory to explore.

I especially liked the choice to use 'as if' in the construction of your premise. I think that it is useful and often necessary to use that construction, in order to proceed with analysis, but I am glad you showed that can be avoided. The trickiest piece is that people adopt limiting assumptions in order to simplify calculations, or to make them tractable; then forget that they are exploring a special or limited case. They proceed as though...

I left aside the question of infinity in my essay entirely, preferring to deal with the concept of boundedness versus unbounded regimes - which I know more about. You took the bull by the horns and grappled with some of the tough issues Eckard. And you acquitted yourself better than many philosophers or top scholars. So you have my admiration for this work.

Kudos!

Jonathan

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Jonathan J. Dickau replied on May. 12, 2020 @ 16:28 GMT
I should amend that.

I said it incorrectly. People make 'limiting or enabling assumptions,' it should be, to reflect the insights in your essay.

JJD

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Jonathan J. Dickau replied on May. 13, 2020 @ 02:16 GMT
And I want to add...

I like that you mention the distinction between thumb and fingers, enabling one to count from 0 to 99 instead of only to 10.

Have Fun,

Jonathan

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Author Eckard Blumschein replied on May. 15, 2020 @ 05:44 GMT
Dear Jonathan Dickau,

Thank you very much for your encouraging comment. I sadly admit that I was not able to persuade anybody, not even you, that there is something very foundational beyond a taken for granted reckoning: At least the late Einstein confessed that “the now worried him seriously”. He felt forced to attribute the distinction between past and future to something outside...

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Author Eckard Blumschein wrote on May. 17, 2020 @ 04:26 GMT
“Calculate as if there was no causality … but ” implies what I wrote to Steven Dufourny:

“Steve, Instead of writing t=0 I should perhaps be more careful and write

t_past=t_future=0.

You (and perhaps many others) did not understand that t_past can be imagined counting for a snapshot the distance backward (leftward) from actual zero toward older events. For the same...

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