Continuation Causes Superior but Unrealistic Ambiguity by Eckard Blumschein

Eckard,

I guess my point would be that R is a set of n-dimensional countables, while only from Q can we get R. Maybe we are agreed.

Doug

Dear Eckard

I hope your plasmonics is getting fine tuned. I find the web and journals about 5 years ahead of most books. I hope you've Googled plenty as well. Recent Optical fibre science is also another hoard of hidden riches. I generally read 3-5 new papers/day, from all subjects, plus the journals. The current (26th) New Scientist p16 has a typical result, showing particles 'bounce' off the plasma fine structure of matter NOT the solid mass itself! Wave particle interaction is fascinating.

You seemed to prejudice yourself against trusting my work with regard to superluminal motion. But I don't think you ever took on board the point about 'apparent' motion, from a different inertial frame, being wholly different to real local superluminal motion which I agree is not possible, and which gives rise to the 'Lorentz' (actually originally Fresnel) exponential curve, which is misused and only has that very limited domain.

If you don't see that; Please, envisage a fast flowing river. You are sitting in your car on the bank observing. The laws of physics say water no water molecule can move at more than 0.1mph. If you drive your car along the bank and video the water molecules at the centre of the stream from your inertial frame would they care? would they be breaking the law? of course not.

But then you stand still and video them, and the centre of the stream is still doing 7mph wrt your camera!! Are they breaking the law? Of course not! Their own 'inertial field' is that of the molecules nearer to the bank each side. No water breaks the law LOCALLY, and no water cares about which planet it's on or who else is moving anywhere. Physicists must learn to renormalise mathematical results back to reality, as all maths, points, lines and vectors, are mathematical. Moving points are not valid in geometry!

So apparent v c should be fine, and it's probably about time physics took that aboard as it seems to be in denial at present, due to lack of comprehension and over reliance on maths. All this is as simply explained by Georgina.

It's implications are fundamental, bypassing Bell to give Reality and Locality, and should be able to move physics on 100 years. You may also look over the last few posts on my string. If you can help by advising on how better you think it may be explained I'd warmly welcome it.

Do keep asking any questions. Sorry got a little frustrated when my carefully thought out answer was apparently just dismissed the last time. 'Apparent' is an important concept!

Best wishes

Peter

Dear Doug,

You wrote:"I guess my point would be that R is a set of n-dimensional countables, while only from Q can we get R. Maybe we are agreed."

The only reasonable to me possibility to clearly and consequently distinguish between R and Q is not conform with the current tenets: While present mathematics declares R also as subject to trichotomy as definitely is Q,

I consider R, and of course R too, a genuine continuum as still described by Peirce: something every part of which has parts. Such continuum can strictly speaking neither be separated into single points, no matter how many, nor can it be an existing set composed of them. Only rational numbers are countable. Consequently understood real numbers are uncountable even if they can be approximated as accurately as you like. They are a different quality.

Correspondingly it is not correct to make a quantitative comparison between R and Q. There are not more reals than rationals because there is no basis for a quantitative comparison between a quantity and a quality. Cantor's paradise is an infinitum creatum, an elusive created infinity, an infinity inspired by the imagination of a huge number.

Dedekind declared the real numbers the union of rational and irrational numbers.

This is only reasonable if one admits that the embedded rational numbers lost their property to be numerically accessible. Dedekind was forced to admit having no evidence for equal treatment. He understood that any two rational numbers must be different from each other but he denied that genuine continuity demands numbers of unimaginable actually infinite precision, which must NOT allow to be distinguished from each other. For instance 0.999... and the fictitious successor 1.000... each with an actually infinite amount of nines or zeros, respectively, differ from each other by nothing.

Since Pythagorean time mathematicians have a problem with their lacking readiness to admit that countables and continuum exclude and complement each other. Having learned to benefit from infinite series, mathematicians of 19th century were not satisfied with the obvious correctness of limits. Now we have several axiomatic set theories that claim to be rigorous but none of them could achieve any improvement. On the contrary, they caused and will continue to cause unnecessary trouble.

All this would not bother me if no "mathematical" obstacles against R did arise from theories based on Dedekind's and Cantor's superficial distinction between rational and real numbers while simultaneous equal treatment of them.

In my essay I gave examples for further shortcomings.

In principle, my suggestions are addressed to mathematicians. However I see they likewise relevant for physics and in particular the given topic. Dedekind was among the first who suggested a discrete (non-Peirce) continuum of space.

Incidentally, at that time, the notion dimension was not the original one.

Regards,

Eckard

I think that when a work is rational ,it can be completed, and sometimes it's not necessary to complete it. Pierce is rational because the numbers rest inside a closed system of distribution, the continuity in this line of reasoning rests logic and rational. In fact it's always a question of domains and groups of continuity. The numbers and their distribution shall be always rational in their series. Cantor is not about a rational continuum due to the confusion between the unknwn and the physicality, the numbers indeed are reals inside this physicality in evolution.

Could you say me more about abduction, deduction, and induction dear Eckard please, I am persuaded you have some ideas, philosophical.....hypothesis, consequences,demonstration after all.....that seems a kind of categorification also in a computing point of vue?

Regards

Steve

For you Eckard, who was the best rationalist, the most rational and logic between these persons, Dedekind, Cantor, Riemann,Gauss,Poincarré,Pierce,Euler,Stern,Dirichlet,Hilbert.

Could you tell me more please also about the zeta function and the relation with pi.The theory of numbers and the continuity is fascinating .....

Steve

Hi, Very beautiful discussion indeed about the continuity and the discreteness. My thought has always been that in fact the 0, the - and the infinity doesn't really exist in the pure physicality. The 1 as unit is essential for magnitudes indeed, the reals are essentials. The spherical distribution seems so incredible , simple and in the same time so complex.For me the 1 is the most foundamental unity,the volumes are correlated.It's incredible the combinations in fact , there the groups and categories seems relevant for applications, now of course the Universe has its specific ultim serie with the real 1 as unit of beginning and x as closed limit.That for all universal finite series,ultim if I can say,Galois perhaps can help.

Best

steve

Dear Eckard,

To my unsophisticated, amateur mind, the idea of rational numbers embedded in a continuum is ludicrous. If we take the number 1 in R, we have two options to consider, one is the operation where we add multiple ones together, and the other is where we divide up the one into multiple parts.

In the first operation, we can continue to add ones to the accumulated total forever, without limit. In the second operation, we can continue to divide up the one into smaller divisions forever.

Clearly, there is no gap between the divisions of 1 that we choose, just as there is no gap between the multiple units we accumulate. However, when we add an x number of y divisions to some accumulated total of units, if x < y, then obviously there are geometric magnitudes that we cannot access numerically.

Nevertheless, it is conceivable that, if we had a workable procedure, we could change our units to an appropriate magnitude in order to access the formerly inaccessible geometric magnitude numerically, since the choice of the magnitude that we use for our unit is arbitrary.

Hence, this demonstrates that the so-called irrational numbers, or irrational magnitudes, are nothing more than an artifact of our choice of a unit magnitude. This does not mean that such an artifact cannot be used to advantage, but it does mean that we should keep in mind that it is called irrational for a good reason.

When we collapse the unit ball to zero, one of the irrational artifacts associated with 1, the square root of 2 (the other is the inverse of the square root of 2), which is the larger radius, ceases to exist (as does its inverse) once the unit radius reaches zero, even though it is a significantly larger magnitude (and even though its inverse is a significantly smaller magnitude).

Is it not so, surely?

Regards,

Doug

Eckard.

It is simply exposed by analogy.

A boat has a maximum speed of 'c' kph. It is moving on a river, which is flowing at v kph. 20 observers (Ob1-20) are given video cameras and told to record it so it's speed can be analysed. The first 17 take the video from cars going up and down the bank, and back and forth over bridges, from trains, cycles, aeroplanes, the space station, the moon, jogging across adjacent fields and from other moving boats. They all get different results!! Ob18 is standing still, on Earth, on the river bank. So.. Does he get the result 'c'?

Of course not he get's c plus v.! ...Ob19 then uses the Hubble space telescope camera! SO... Does he get 'c'? ...Of course not - he gets c plus v plus v2(=orbital v of Hubble).

So.. one left! Ob20 is the only intelligent life form. He jumps into the water, or onto another boat, and float at rest wrt the water, videoing the boat as it comes past close by (LOCALLY), and his result gives precisely 'C'.

The stream from the Quasar is the river. it has 'incentric' (graded) motion, going slow beside the bank and fast at it's centre. (There are some super cross sections through the jet streams from spectroscopy in some papers on the web). In all this time the boat was complying with 'c' and knew nothing of all the fools rushing around with cameras, who might as well have been on another planet!

Was that understandable?

The sq root formulae was originally Fresnels, for another (proper) purpose. The term was wrong, is there a handy term for the infinite curve produced?

I DON'T actually prefer a 'digital' field theory. Nature may be called whatever we wish but the model consists of an unknown condensate field of energy potential which is of limited compressibility, equivalent to Edwins 'C' field or the old 'ether', so may be as continuous as the waves it propagates. When perturbated or compressed (by meeting a medium doing 'a' relative speed) particles are condensed. These are initially ions, i.e. a plasma. These then impliment the change in f and or lambda (subject to which way the observer is rushing around with his camera!) to maintain 'c' and conserve E locally within the new co-moving medium. These ions can bunch together to make more or less intelligent life forms and their houses.

i.e. Matter would not exist without discrete particles, but the field they condense from is continuous. It is not however entirely a continuum! as it is in what might trendily be termed 'blocks' of continuum. Whether we call a wave continuous is semantics! (see Ken Whartons excellent and very readable essay).

If you'd like any of the evidence follow the references or do just ask.

This is mega paradigm changing stuff you know!

Best wishes

Peter

Thank you very much dear Eckard for this beautiful aswer and explaination.Me My Favorites are Borh, Newton , Gallilei and Euler.

I agree about the works of Pierce, it's very inetersting and relevant, as what the rational logic will be always the best road.

The interpretations of the physicality can be made by maths if and only if the real domains are inserted with their pure finite series.

In all case, you are a real searcher of truths and truth.Thanks for that and for your knowledges.

Best Regards

Steve

Eckard

O posted a reply on my page but it didn't seem to go through so I will post it here.

Yes I read your essay but I confess I did not give it proper thought the first time. I apologize to you for my posting as it was not well taken and you are absolutely correct in being disturbed.Your essay is very good and your points well taken.I shall endeavor to read further essays more carefully.

Tom Wagner

Dear Eckard

I am sure which might be the better place to submit a post so I am submitting to both our sites.

Thank you for alerting me as to the rating system of which I was unaware. I will certainly now reread your essay (I have been fighting some deadlines here so I could not give this entire project the attention I would like. I am now going to take the time to read some of the other essays as the interplay between those of us who entered essays seems to be the most interesting part of this whole experience.

Tom Wagner

Dear Tom Wagner,

Having read several essays, I realized that almost nobody besides me addressed not merely continuous vs. discrete but literally analog vs. digital models.

Accordingly most readers of my essay did perhaps not understand why I consider already DEQs the first step into ambiguity and complex representation twice redundant. The reasons for me to thoroughly deal with history of mathematics were mainly paradoxes not just in physics but also already in mathematics.

I pondered about the possibility to restrict the scope of my essay as not to lose all readers. However, even if I was not in position to explain in detail how the many uncommon alternatives to established tenets are interrelated, this mutual dependency is important.

What about the chance of getting these alternatives taken seriously, I so far hoped in vain for arguments that challenge me, and I can imagine how FQXi cautiously anticipates reactions of those who are definitely unhappy with what they will feel wrong and an attack on their theories. Not all posts are immediately shown. My votes did not change the indicated rates and numbers of public votes. Nonetheless I highly appreciate the opportunity to take part in a polite factual discussion without taboos.

On the other hand, I consider most of the alternatives well founded, and I expect the outcome of LHC providing further support for my criticism. In the meantime, I can only collect further indications.

Regards,

Eckard

Dear Eckard

I have reread your essay and I do have a better picture of what you are saying. While I do have a fair layman's grasp of the study sub-atomic particles I do not possess the sophistication nor the experience in such matters to allow me to engage in a meaningful debate. I plan to read it again as there is much included that stimulates ideas.

I was struck by your reference to Sommerfeld on page four. When he states that no wave is reflected from infinity in finite time sounds a bit like the notion that a moving object cannot transverse an infinite number of points in a finite amount of time. Be that as it may, I am more interest in the next statement, Standing waves are strictly speaking approximations.

A standing wave is a very definable and precise physical phenomenon. It is the initiator of most and perhaps all sound. This can best be seen in a musical example. More than half a century ago, Frederick Saunders wrote an article about the physics of music for Scientific American. This article had more errors and misconceptions that I have ever seen in one article. Saunders was a noted figure in the acoustical world, but physicists are only human (at least most of them are).

One false assumption that most people make about the generation of a music as sound, and I use Saunder's example of an instrument such as a clarinet or an oboe, is that it is the movement of the traveling longitudinal wave that transverses the from the mouthpiece to either the end of the instrument or to the first open key actually creates the sound.. A conjugate is returned and wave moves back and forth through the instrument.

Saunders makes the statement that it is the air that flows in and out of the finger holes that creates the sound. He then went on to state the fundamental is the only note whose sound goes out of the end of the instrument. If this were to be true then why do they put bells on both clarinets and oboes if they only affect a single note?

The movement of the traveling wave back and forth sets up the frequency of the tone. The structure of the sound begins in the reed of either instrument. This is fed from the mouthpiece to the sides of the instrument. The movement of the air creates a classic standing wave, which is modified by the information residing on the sides. The severe impedance mismatch between the air and the materials from which an instrument is created means that the body of any instrument contributes little to the sound we hear. The primary interface that creates the sound lies across the plane of the open end of the instrument. This is why a bell increases the volume of the sound; it increases the area of interface.

This is true of most instruments. The standing wave that forms in the body of most instruments is a resonance. Perhaps the biggest obstacle in understanding sound is the lack of understanding that a vibration and a resonance are two related but decidedly different things. Any material with some elastic properties will resonate to any frequency. Only if the resonance is near to the overtone structure of the resonating material will that material vibrate. On the other hand, a vibration is necessary to create the resonance initially. Both the vibration and the resonance are digital.

Sound is not a single isolated occurrence; it is a process that ends in the Organ of Corti. The Organ of Corti is a fluid filled canal in the cochlea, which houses the hair cells that stimulate the nerves to the brain. The final argument for hearing being a discrete process is that the messages the nerves send to the brain are in the form of discrete pulses. They respond to an increase in amplitude by sending more pulses per unit time.

Since all of the nerves that send data to the brain are quite the same we have to wonder if all sensations are transmitted to brain as discrete pulses. While I agree that the brain is not necessarily just a big computer we have to be aware of the fact that the complex of nerves that address the brain do behave a bit like a computer bus and the pulses are, in effect, bit patterns.

Thanks for a very provocative essay.

Tom Wagner

Dear Tom Wagner,

Please do not take it amiss that I added Wagner. Tom alone is perhaps a too frequent name. You need not telling me acoustics. While my dissertation, forty years ago, was a comparative study of power electronics for arc welding, the superiority of welding by ear challenged me. Maybe you know the English professor and self declared pop star Chris Plack. It was he who told me that there is a Steven Greenberg of ICSI Berkely who uttered similar ideas on the mechanism of hearing as I suggested. The latter argued correctly that a frequency analysis alone could not explain the astonishing performance of hearing. For instance, onset is utterly important. Steven Greenberg organized together with Malcolm Slaney of Stanford an Advanced Study Institute on Computational Hearing in 1998 in Il Ciocco, Tuscany, and invited me to take part. Here I met virtually all important experts on hearing. Since then I thoroughly dealt with auditory function.

Certainly you know the huge list that was initiated by Al Bregman and is maintained by Dan Ellis. Al Bergman asked for altruists as to get his list rid of too controversial discussions. Jont Allen and I each provided a forum.

I intended to find out how the extraction of temporal features from sound might work and how to explain why the spectrogram has so many shortcomings. In the end I got increasingly aware of a cardinal mistake in theory of signal processing:

Complex analysis and inclusion of void future data is a detour.

Meanwhile I also got familiar with many details of the physiology of the auditory pathway up to A1. In Magdeburg we have a Leibniz Institute of Neurobiology. Moreover I regularly attended the annual meetings of DAGA (German Acoustics Society) and read JASA as well as ARLO papers. Currently I am just participating in a list on Cochlear Amplifier by Matt Flax.

What about my statement that standing waves are strictly speaking an approximation, I should add that I was teaching fundamentals of electrical engineering for decades. So you may consider me a professional in this field.

You wrote: "A standing wave is a very definable and precise physical phenomenon." What I meant refers to the fact that every signal in reality has a beginning and an end. We may describe it as a superposition of a transient and a stationary component. Neglect of the former is an approximation.

If I did not sufficiently answer your question, please do not hesitate asking again. Questions by laymen are often valuable. We need not be able to follow for instance Lawrence Crowell as to find out why the theory of "relativity" and non-relativistic quantum mechanics do not fit together, why quantum computing does not work, and why so far neither the Higgs boson nor SUSY were experimentally confirmed.

Regards,

Eckard

Regards,

Eckard