Continuation Causes Superior but Unrealistic Ambiguity by Eckard Blumschein

Dear Escard,

You cannot prove that the world is analog, digital, or analog-digital by analyzing signal processing, complex calculus or mathematical laws. And the discussions about history of physics (Zeno, Aristotle) proves nothing. To prove that reality is analog, digital, or analog-digital you must analyze the structure of spacetime and matter, but not complex calculus or the history of physics.

Sincerely

Constantin

Dear Eckard-

Thanks for taking the time to read my essay: Is Reality Digital or Analog? by Joel Mayer, MD. Our goals are seperate in that my interest is the quantum mechanics of cell production while yours seems to be the mathematics of electrical engineering. Yet, it helps me to read papers by someone with your background. As from your words I can learn how to make a better impression on physical scientists. Do you have a blog? May I have a link? I need to study your papers! joelm_armillary at msn.com

Dear Joel,

Mathematics of electrical engineering is my background rather than my prevaling interest. You will find my last refereed by IEEE paper and my homepage in the references I gave to this essay. I also recommend my

previous essays.

When I started with my homepage, I responded to Al Bregman who aked for altruists as to remove a special debate on auditory function from a huge list devoted to all auditory matters. I am a bit ashamed for neglecting my homepage.

The reason for me to do so is my intention to contribute, within the few years I may still hope to live, perhaps essential corrections to some very basics of mathematics and physics I got aware of. I consider them the key to a better understanding not just of cochlear function. While I am still in contact with all leading experts of this very special field worldwide, most of these individuals typically tend to adhere each to his own ideas or celebrate their heros. I do not expect a better situation here among physicists. Nonetheless I will try my best to get understood. Thank you for reading my essay.

Regards,

Eckard

Dear Eckard Blumschein

Thank you for read my essay.

I think, you are misunderstanding something. You cannot separate mathematics and logic. If you are saying you have found some problems with some basic notions in mathematics it is because the logic that you are using to think about these notions do not agree with the logic that define and govern them. I read your essay and what you see as problem is because you are unconsciously denying the excluded middle principle of classical logic that allows to abstract numbers with the limit point of the extension they represent. I agree with you extensions are more fundamental, but what you are ignoring is that if you say we should not identify extensions with its points, what are you saying is that we shouldn't use classical logic to describe the continuum, that kind of misconceptions is what my essay is about. On the other hand you don't need a quantum computer to justify that quantum reality is ruled by a non classical logic, you just need a half-silvered-mirrow and light to construct a a machine that cannot be described using classical logic. I hope you will read again my essay and try to understand that my point agrees with yours in many points.

Regards,

J.B.

Dear John Benavides,

Thank you very much for providing me a chance for taking issue against unfortunately mandatory arbitrarily settled tenets. I appreciate that you are dealing with a topic that is with roughly Dedekind's words difficult and (seemingly) marginal. I see some important implications. And, well, your 'point' agrees with mine in many 'points'.

When I finished my essay it was too long. So I decided to omit my somewhat constructivistic position concerning trichotomy and the TND. As a mathematician you should know that Brouwer got aware that the TND is only valid in Q, not in R.

From your name I guess, you are perhaps not in position to read German. Otherwise I would recommend to you a nice historical survey by Oscar Becker and books by Gericke.

What about the missing logic in quantum theories as expressed by Feynman, I would like to go into the nitty gritty and learn what is wrong. I am convinced having found a serious mistake made in 1925. I am also pretty confident that quantum computing and Higgs boson are based an at least shaky ground.

Please tell me why you are believing that a half-silvered mirror contradicts classical logic. I am aware of several experiments. Don't you take the possibility into account that something you learned to imagine might be simply incorrect?

Didn't Cantor ignore the 4th logical possibility? Wasn't Galileo Galilei correct?

I do not say we shouldn't use classical logic. I maintain, any really real number is as fictitious as is an irrational one. We must not believe to be able taking it away separately.

Regards,

Eckard

Dear Eckard

I recommend you to read the paper of Deutsch and Lupacchini that I cited on my essay, I am sure you will enjoy it even if you will not agree with their arguments, it is a short and very nice paper. There you will find why I think classical logic is not appropriate to describe quantum reality.

Dear John Benavides,

I did not yet manage getting D. Deutsch, R. Lupacchini, Machines, logic, and quantum physics, Bulletin of Symbolic Logic 3 , September 2000. While I esteem Diana Deutsch an excellent expert, I am not sure whether the work by David Deutsch has a sound basis. I already uttered my doubt that quantum computing will ever work as promised, not for the excuses aired in a previous contest but possibly due to a fundamental mistake. What about formal logic, I abstain from layman's guesses. I merely criticize obvious to me inconsistencies in fundamentals of mathematics.

Let me give examples:

Dedekind himself admitted to have no proof for his famous cut. The devil is already in his basic assumptions.

Cantor might have got insane because he was unable to provide an already announced proof.

Kronecker understood that G. Cantor was wrong. When David Tong wrote "... everyone disagreed with Kronecker" he was unfortunately right. Kronecker's tragic was, he also intended to perform the impossible: Arithmetisierung of the continuum. Cauchy and Weierstrass preferred to build on Leibniz's pragmatism. Irrational numbers were already pretty well understood by Martin Luther's friend Stiefel. The naive elusive alephs by G. Cantor caused nothing but unnecessary trouble. Or can you give an example for any use of aleph_2? Having uttered this criticism privately, I often heard: We know, Cantor ... However. Even Ebbinghaus evades in public to call a spade a spade. Read his Lessing quote.

My position is quite clear: While real numbers must not be understood as rational numbers of very high precision as the actual infinity must not be understood as a very large number, it is nonetheless absolutely legitimate to treat them like rational ones because the difference between R and Q is only relevant if one tries to single out a particular number.

I dislike books for engineers that illustrate the function |sign(x)| v-shaped going down to zero for x=0 "for mathematical reasons". This is a benign but unfortunately not the only nonsense.

While I highly appreciate H. Weyl's honest admissions:

"We are less certain than everabout the ultimate foundations" and

"at the moment no explanation is in sight" (for PCT symmetries),

I cannot agree with his metaphors calling the rational numbers bones embedded into the sauce of reals. Well, the sauce is a good metaphor. However, the number five of rational numbers has lost its accessible identity among consequently understood reals. It is no longer a bone.

I guess, I understand well why mathematics refuses accepting logic. My suggestion the reinstate Euclid's notion of number more precisely as a limit measured from zero might hopefully provide a way out the calamities.

Did you understand my points?

Regards,

Eckard

Doug Bundy pointed me to a "clarification" by John Baez. I did not find it and asked in Physics Forum for help.

A. Neumaier replied concerning what Andy Akhmeteli and I found out independently of each other: "In principle C is not necessary even for quantum theory-"

He argued: "It might be sufficient in principle but forcing physics into the Procrustes bed of banning C would make many things very tedious - from the Fourier transform to creation and annihilation operators. How would one write the canonical commutation relation [q,p]=i hbar without using complex numbers?"

The answer can be found in my essay:

C is definitely superior but redundant. R and the cosine transform are sufficient in principle. So called "verschaffte Quantisierungsbedingung" can be written as 2 pi pq/h - 2pi qp/h = i as to understand that Plancks constant h has nothing to do with i and commutation. Both the imaginary unit and the property of non-commuting are redundant artifacts due to complex Fourier transformation from one-sided reality into the Hermitian symmetry in complex domain. Notice: Fourier transformation is based on an arbitrary omission. This and its consequences is surprising to experts of quantum theory. Nonetheless it is true.

Eckard

Hi Eckhard,

I'm sure it was on Baez's site, n-category cafe, where I was reading it. For instance, he writes about metric spaces and says: (see here)

"Let's start with a simple observation. Steve Schanuel has a paper 'What is the length of a potato?' in which he points out that a closed interval of length 1 centimetre is not very good as a ruler: if you put two of them end-to-end then you don't quite get an interval of 2cm - there's a point in the middle left over. A half-open interval would be better. Thus, the measure of the closed interval isn't really 1cm: it's 1cm+1point, or 1cm1+1cm0, or simply 1cm+1. Similarly, a closed interval of length acm has length acm+1."

I don't know if this is what I remembered now or not, but at least it's a place to start.

The link was broken by an extra space. Let's try again:

http://golem.ph.utexas.edu/category/2008/02/metric_spaces.html

Dear Eckard,

Again, is it not a problem with defining a point? There must always be room for the concept of nothing, but how something can be located to the left of nothing makes no sense at all, unless we are talking about motion, locations and directions. I'm reminded of the "crying jag" that Lorna Sage had when she was a child, as reported by Sean Carroll several years ago, when he was discussing the doorway leading to the bewildering consequences that makes things so murky today. (See here)

W.R. Hamilton had similar misgivings about negatives and imaginaries, which he sought to eliminate by basing algebra on motion, instead of fixed forms. But as you point out, engineers can't afford to mess around with bewildering consequences. When they discard one of the side bands in SSB transmission to eliminate the redundancy of info in their transmissions, they are looking for practical results.

Nevertheless, when the redundancy is part of the symmetry of nature, as she is always balancing her act, I think it's an important objective to understand how and why she does it, even though that understanding may not have practical consequences in the short term.

When Dirac had the sudden insight that connected Heisenberg's "strange" multiplication with the familiar Poisson brackets, the physics community was trying to solve the real problem presented by real experiments. They could not, of course, see the day when the use of Lie algebras of Lie groups would run into trouble trying to extend their ideas into three dimensions.

The concepts of C and R- have worked out well for physics, and C has worked out well for engineering, in a practical sense, even if philosophers have been left bewildered and confused. For a philosopher, understanding is usually a matter of clearing out the fog, but when the fog keeps pouring out of universities and labs as it does in modern times, the hapless philosopher can only retreat to a cave and try to clear his head, as best he can.

In my cave, I contemplate the tetraktys. It starts with 20 = 1, implying that rational numbers are primordial. If so, then 2/2 = 1 must have some profound significance, and if that signicance lies in the symmetry of reciprocity, then the concept of inverses is a crucial one. As I touched on in the discussion of my essay, it is useful to think of 2/2 = 2(1-1) = 20 = 1, as 1/1, where the equality of the numerator and the denominator denote a difference of 0, as well as a quotient of 1.

When we take this ratio view, then there are definitely two real "directions" possible, with respect to 0, the negative ratio 1/2 and the positive ratio 2/1, on either side of the unit ratio, 1/1, which is equal to unity, because their is no difference between numerator and denominator. The difference, or imbalance of 1/2 can be expressed as -1, the lack of difference, or lack of imbalance of 1/1 can be expressed as 0, and the difference, or imbalance of 2/1 can be expressed as +1. So, we have -1, 0, +1, with no issue remaining as to which "side" we should assign nil to, and the fact that there is a two octave spread between them suggests that the c limit in physics may be misleading, in some cases.

Just some thoughts to share with you.

Regards,

Doug

Dear Doug,

Yes, yes, and yes with minor caveats. I intend continuing my other posting as promised but not yet immediately. Then I will explain why I consider the current interpretation of real numbers a chimera.

Thank you for reminding me of even more reasons to get aware that sometimes the idea "a number is a number is a number" has unacceptable consequences. Before Terhardt wrote his updating of Laplace transformation, he faced notorious rejection of his justified criticism from all peers. Your argument is absolutely correct while the use of located and location is seemingly self-contradictory:

"how something can be located to the left of nothing makes no sense at all, unless we are talking about motion, locations and directions".

I would rather prefer to say: There is no negative distance in reality, and no effect precedes its cause. Non-causality is always unreal.

I was happy that my students did not ask me how to apply the picture of a symmetrical delta impulse on a one-sided radius scale at r=0. While I hate pretending, I nonetheless felt obliged to not deviate from mandatory theory.

What about C, my point relates to the tacit use of an arbitrarily chosen omission, of mostly either the clockwise or the anti-clockwise rotating phasor. Euler's equivalence is no problem at all. Heaviside's continuation demands the correct return to the original one-sided and real domain.

Admittedly I do not quite understand what you meant with "cave". And of course, log(1)=0. A measure in dB is not the original one.

I am not familiar with Hamilton. Did he continue the old fluentist ideas which were used e.g. by the Pythagoreans, Aristotle, Cavalieri, Torricelli, and Newton?

I don't see Dirac responsible for the double redundancy in quantum theory. Already Poisson and later on all experts around Heisenberg including Kramers, Born, Pauli, and Jordan took the unrealistic bilateral time scale from minus infinity to plus infinity for granted. Accordingly, Schroedinger/Weyl used to choose a complex ansatz.

Regards,

Eckard

Thank you for you essay. It is good to see people who are passionate about their field, since it brings about good discussions. I have a few remarks about the content:

1. Page 1. Analog computing is outdated. It was immediately bound to the real behavior of lumped electric amplifiers, capacitors, and resistors. Its results could be wrong, e.g. due to ignored invariance laws.

What kind of invariance laws are you referring to?

2. Page 1. Some phenomena can better be described by continuous "analog" models, others by discrete models.

There are also models which have a combination of discrete and analog aspects. Think about a clock, which has both continuous and discrete behavior: continuous behavior between the ticks and discrete behavior at the moment the tick is produced.

3. Page 2. quantum physicists are trying to derive from created mathematics a completely discrete structure of reality.

This is partially true. The Schrodinger equation has a continuous solution. If you talk about particle models, then it is somewhat correct. Both particles and interactions are modeled as discrete entities, often involving never directly observed virtual particles. I think there are major issues with that approach.

4. Page 7. When Minkowski's introduced ict as fourth dimension, he confessed not to understand why it is imaginary.

There is no real need to introduce imaginary time. It leads to more convenient mathematical expressions, but moves away from the underlying physics. See my essay for an impression that i is not needed. On my website I have a report that derived the Lorentz Transformation without ever needing i).

5. Page 7. Planck's constant h is just required as to get a dimensionless argument. It may be called quantum of action, but it has the meaning of the smallest quantum of energy E=h-bar*omega only on condition there is a lower limit to the circular frequency. Wave guides have such a cut-off frequency for transversal waves.

The expression and cut-off behavior is, I think, correct for the case of waveguides that you mention involving photons. However, unlike for electrons, the quantum of action of photons is equal to zero (E=pc gives 0=Edt-pdx, where c=dx/dt, for free electrons: h=Edt-pdx, more details on my web site). The expression E=h-bar*omega should really be read as omega_photon=dE/h-bar, where dE is the change in energy of an atom when the photon is emitted. Conservation of energy then says dE_atom = E_photon such that E-photon=h-bar*omega_photon, where h still pertains to the atom. E-photon=h-bar*omega_photon can be less formally written as E=h-bar*omega. So, although the quantum action of a photon is equal to zero, the expression E=h-bar*omega contains h. Lot's of details, but important for correct physical interpretation imo.

Best regards and good luck with the contents.

Dear Eckard,

While there is no negative distance in reality, there definitely is a left and right, an up and down and a backward and forward, relative to a selected position, and since space is usually defined as a set of positions satisfying the postulates of geometry, I think it important to not throw the baby out with the bathwater.

Sir W. R. Hamilton was an English astronomer and mathematician who coined the term "vector," first explained complex numbers as coordinates on a graph (or rotation made possible by an imaginary number), and is credited with the invention of quaternions (even though a Frenchman beat him to it and understood the true nature of quaternions better).

It was based on his ideas that Pait, arguing for Hamilton's quaternions, took on Heaviside and Gibbs, and lost the battle with their vector algebra, which has dominated ever since.

However, quaternions found a new life in computer calculations, since it greatly simplifies the manipulations of 3D rotations and avoids gymbal lock. They were mostly revived by David Hestenes, who first recognized the value of the ideas of Grassmann and Clifford and popularized them through his modification of Grassmann's geometric algebra (GA) (see here).

GA is slowly gaining acceptance, since it greatly simplifies vector algebra through the use of new concepts and definitions that combine scalars and vectors in something called the geometric product. It has to do with rotation and an inner and outer product.

As I mentioned, it was Hestenes' work on GA that drew attention to the work of Hamilton, Grassmann and Clifford, and it was mostly centered on the set of Clifford algebras upon which his work sheds so much light.

This lead me to a little known essay by Hamilton that is called "Algebra as the Science of Pure Time." Most people think that it was based on Kant's ideas of time. I don't think it has anything to do with the Greek concept of the continuum as a moving point.

It focuses on the comparison of moments of time, where we can say that two moments may be coincident, or else one is later or earlier than the other. Of course, his development was confined to the observer's frame of reference in the abstract.