John,

I believe that an objective reality exists. I'm not so sure about it being finite, or at least having a finite information content; even if the cosmos consisted of just three "points", the ratio of distances between those points may be represented by some real number, with an infinite number of significant, incompressible digits. But more importantly, human observers can "behave" towards their own measurements and observations, in ways that are "symbolic", rather than physical; it is not the mass, or electric charge, or energy or momentum etc., of a printed text, that drives the behavior of a human capable of reading that text. In short, we "interpret" our measurements, and our theories predicting future measurements, just as we interpret texts. We believe that they are telling us something other, and more significant, than just the numerical value observed. Thus, we may as Tom has said, make "exact measurements", but that need not imply the existence of any exact or unique "interpretation". The reason we stop at red traffic lights rather than green ones, has little to do with physics. Unfortunately, the same can be said about most physical measurements - their values may be exact, but the meaning assigned to those values (it means reality is non-local!, it means there is no free-will!, etc.) is far from exact or certain.

Rob McEachern

Thanks Rob,

I appreciate the time and attention in your response. I'll 'watch and learn' if you don't mind, I'm going through some changes presently. jrc

Rob,

Why didn't you get my point? MP3 benefits from DCT which stands for discrete Cosine transformation in contrast to DFT where the F means Fourier.

You are quite right; the data on consideration must already be "in hand". Future data can definitely not be measured even if their sequence may be expected for "sure" like the Amen in church. They would belong to the realm of block-time which the physicists are still imagining to arrange even all future events along an a priori existing time scale from minus infinity to plus infinity. Heaviside managed to make FT applicable as if future date were available in advance.

Discrete representations including DCT are genuinely lossy in the sense their resolution depends on a chosen sample rate. DCT is moreover also lossy in the sense it avoids redundancy. Being a real valued Cosine instead of complex valued Fourier transformation, it avoids the mirror data that belong to Heaviside's trick of analytical continuation which is a precondition of any application of Fourier transformation on measured data, no matter whether a discrete or a continuous FT is used. This loss of unnecessary data does not mean a loss of original information but merely of the arbitrarily chosen and therefore irrelevant point of reference which is unavoidably implied in any conventional (event related) time scale. Our ear is not synchronized to midnight in Greenwich. The only objective point of temporal reference is the very moment, the now.

Decades ago I did not yet understand this. So I wrongly mistook the fact that the ear is highly phase deaf and asked myself: Why doesn't audition take advantage of so called phase information?

Fourier dealt with heat conduction within a ring. Obviously, such ring model doesn't fit to the world. Heaviside quasi squeezed the ring into two mirror-symmetrical halves, the past and its mirror picture as a substitute for the missing future. I see the Fourier-Heaviside formalism in signal processing and in physics as valuable but not always justified detours. DCT is superior to DFT.

Eckard

Eckard,

I do understand your point. But I do not see the point as being of particular significance.

For example, you said that "Heaviside managed to make FT applicable as if future date were available in advance." It has little to do with what Heaviside did. It is applicable to ALL data, past, present and future. But the data has to be "in hand". So how can data about the future be "in hand" before the future even exists? Easy - if the data is perfectly predictable. The future value of all constants are perfectly predictable. That is why physics is so concerned with "Conservation" laws. Periodic motions are also predictable. That is why physics is so concerned with periodic phenomenon. Such predictions enable integrals, like the Fourier integral, to be integrated over the "prediction in hand" (like Tom's closed-form model of the future), rather than any actual, observed data. It all works just fine, when applied to predictable behavior, like orbiting quantum particles and planets. But it does not work when applied to unpredictable behaviors, like the behaviors of observers with free-will. That is why QM has such big problems, when it claims that the wave functions ought to describe the observers, as well as the observed; the observed may have predictable futures, that can be integrated over, but the observers do not. It is easy to predict that future of Schrodinger's dead cat - it will remain dead. But it is not so easy to predict how an observer will behave when they observe the dead cat.

Coding techniques like MP3 and JPEG, do not just remove the "mirror data", they also eliminate information that the auditory and visual systems are highly insensitive to, even though they contain a great deal of information that a different type of detector, can easily exploit.

The auditory system is largely insensitive to phase information, because the system's detectors cannot respond fast enough to accurately measure it. Instead, it measures amplitude modulations, and transduces those into pitch (correlated with instantaneous frequency) modulations.

Neither the DCT nor the DFT is a good way to model sensory perception, because sensory systems are mostly sensitive to "report" only the modulations of the received signals, rather than the signals themselves. Unlike the case in physics, it is precisely the measurements that are NOT constant and NOT predicable, that conveys the information needed to keep the system "alive". That is why your visual system does not work like a spectrometer - the sun's spectrum does not change, on a human time-scale, hence, measuring it, over and over again, day after day, year after year, serves no useful survival benefit.

Rob McEachern

Rob,

Writing [FT] "is applicable to ALL data, past, present and future. But the data has to be in hand" you didn't get my point. In reality, future data are not yet available, not in hand. Tom's model is unreal. Shannon expressed my view when he distinguished between the unchangeable but known in principle past and the steerable but never completely predictable future. In contrast to Einstein and his followers, Shannon didn't disqualify himself by referring to the present in this context.

When Rao, Ahmed, and Natarajan invented DCT forty years ago, they were well advised to not reveal the fact that Fourier's ring corresponds to the metaphysical mistake of Parmenides. Perhaps they were not even aware of this background. Up to now, most experts tend to belittle cosine transformation as just a special case of the mandatory Fourier transformation.

I mentioned MP3 because this application of cosine transformation is very popular and related to obvious facts: Future sound cannot be heard in advance; Time scale of the ear is not synchronized; Complex analysis cannot be performed in cochlea where OHCs act like one-way rectifiers; FT based signal processing implies non-causalities; Etc.

In case of JPEG I don't consider this foundational background so easily to be seen. When I came up with my suggestion referring time to its natural zero, the very moment, my boss refused to judge it. He meant this is "sowas von fundamental" (utterly foundational). His boss wondered why I compared elapsed time with the likewise always positive radius.

Eckard

Eckard,

"Future sound cannot be heard in advance;" I agree. But the future value of a constant can be known. Some things can be reliably predicted. Those things are the domain of physics. Other things, like the behavior of an observer, cannot be reliably predicted. Those things are not the domain of physics. The problem is, many physicists believe that they are. Obviously observers must obey the laws of physics. But that is not quite the same as saying they do so in a predictable, deterministic way.

The auditory system does not use anything remotely like cosine transforms, anymore than it uses Fourier transforms. Hence, the characteristics of such transforms has little relevance to understanding the auditory system.

Rob McEachern

No Rob (1):

I maintain, the distinction between application of CT or FT is relevant, not although but because CT is a particular case of FT. Application of Fourier's complex transformation is based on adding an arbitrary chosen point of reference. Well, the complex-valued representation conveys the same information as does the original real-valued one. However, the unnatural arbitrary reference to the conventional zero doesn't just make calculations less efficient by adding unnecessary data. More importantly it violates causality. This parallels Einstein's Poincaré synchronization.

Eckard

Rob,

In my first essays I offered a CT based spectrogram that is not noncausal while all FT based spectrograms show more or less obvious an output before any input. I consider causality more natural. You repeatedly mentioned filters. I am not sure whether you refer to physically real ones or to unreal FT based mathematical models.

Eckard

No Rob (2),

You merely admitted that future sound cannot be heard and ascribed this to perception. Einstein even called this a stubborn illusion. I am arguing that observers do not matter in this respect. Causality must be assumed independently.

I looked at a video that tried to show why in (Einstein's) physics there is no distinction between past and future. It was longish and used horribly loud inappropriate statements instead of serious arguments. Where was the fallacy? The video showed how to imagine spacetime. I see this a logical circle.

Eckard

Eckard,

"I am not sure whether you refer to physically real ones or to unreal FT based mathematical models."

Physically real ones, based on the mechanical properties of the inner ear and the subsequent neuronal connections; these have nothing to do with any type of orthogonal function transforms. Since transforms require entire blocks of input data, before they can even begin to process the data, the resulting time-delay, in detecting threats, would be lethal.

If one believe's in classical determinism, then there is no real distinction between the past and the future, everything about the future is determined by the past. I do not believe in such determinism. I have stated why, in several other fqxi web-pages, but it boils down to this:

Determinism is founded on an assumption that is very probably false; that it is possible, at least in principle, for a subset of the cosmos to contain the entire information content of the entire cosmos.

Rob McEachern

Rob,

While I agree in principle on "everything about the future is determined by the past" I share your objection: "Determined" in the sense of causallyelated must not include obviously unreasonable aspects of determinism like denial of free will up to fatalism or considering anything like a calculable model. Any preparation of an experiment is subject to a huge amount of possibly unseen influences. It does not matter whether they are just unseen or erratic. As a student I was told: There are no absolutely closed systems in reality. Models are always just lossy abstractions from far reaching reality. That's why I see the written for good past a realm that essentially differs from not yet real in the sense of not yet actually evolved and therefore unknown future.

Bluntly speaking: In particular some physicists naively confuse their abstract theories with the admittedly only conjectured comprehensive reality. Do future events influence the past? Strictly speaking definitely not, although there are e.g. self-fulfilling prognoses and the like.

I maintain that a real-valued description is in principle sufficient although often not optimal for anything already real.

Eckard

Eckard,

I agree that "a real-valued description is in principle sufficient although often not optimal...". It is easier to multiply complex exponentials, by simply adding their exponents, than to have to remember all of the trigonometric identity functions, required to multiply real-valued trig. functions. That seems to have been the primary consideration, for the introduction of complex arithmetic, for evaluating the "superpositions" of trig. functions, appearing in Fourier analysis.

Rob McEachern

Yes Rob,

A textbook Fourier Acoustics reveals that real-valued representations may require many superimposed cosine components with alternatively positive and negative signs. However, I don't consider the corresponding poor convergence a reason to abandon causality.

Look at the bell-shaped Gauss function that extends symmetrically between minus infinity and plus infinity. While it provides an excellent approximation of a spreading wave, it would be nonsense to infer that the response of air to a blast begins already before the blast. Instead found my guess confirmed by measurement that the wave initially looks like the letter N and gradually changes into its characteristic bell shape.

Let's be cautious with unwarranted generalizations and pointless EPR quarrels. Sound philosophy may often be superior to guesswork like symmetry principles. Causality but not lazy determinism is the indispensable precondition of physics.

Eckard

Eckard,

Nice visualization of the letter N. Correlating to a time dependent energy level change in the emitter particle as the progentitor of a linear projection emerging from a spherical static electromagnetic domain, is perhaps the implied next question. Any guesses there? Guesswork has its place as long as we subject it to rigor. jrc

John C, Rob,

Not just I measured the so called N-wave in case of sound. I am sure: Not even Rob understood why I am convinced that sinus functions, circular symmetry, oscillation forever, etc. are idealizing approximations that do strictly speaking not at all agree with reality. Well I was influenced as a school boy when I read that apparent circles are rather spirals. There are no undamped oscillations. Later I got aware that nature seems to exhibit many pretty good spherical symmetries but rarely circular ones. That's why the sine function that extends from t=-oo to+oo is strictly speaking unreal while sinc for t>0 is not. Nature can be described, in principle, without sin components, Fourier transformation, complex calculus and all that. Don't shy back from the consequences including triangular (half-) matrices.

Rob and many others are just focusing on the astonishing relations between sinusoidal and exponential functions. A damped sin function may be considered as containing an exponential component that makes it realistic and therefore equivalent to superimposed pure cosine components. A pure sin function can of course not be written as a sum of cos functions. This is however not necessary as to correctly describe nature.

Eckard

Eckard,

You have condensed quite a lot, into two brief paragraphs! Where do I begin!?

The point you make is that: realistically it should be obvious that the vertical bar of the N is the origin in the time parameter of the physical wave which we measure. I agree absolutely. It is in how we can measure anything experimentally that makes it all fuzzy, because what we get as the result is physically the response in the field of a detection device, and can only surmise from what we do know without presuming on what we do not know, what constitutes the real physicality of the wave itself. In fluid hydrodynamics, such as acoustics, we can at least observe something of a medium through which the wave propagates. BUT, we can only use that as an approximation of the physical dynamics of an electromagnetic wave which propagates on its own across free space devoid of any medium. And which when encountering any sort of medium, interacts in several ways to either be absorbed, refracted or reflected. Allow me to start by distinguishing that we can only allow that a planar traverse wave is applicable to what would correlate to the surface response of fluid such as water.

If we are observing the translation of a wave from an aspect perpendicular to the longitudinal direction of propagation, the sinusoidal shape of the wave is evident as the signature of a rise and fall of effective response in the detector. If we choose the wave to be a planar transverse wave, that sinusoid is in reality a cross-section representation. But, we can rotate our position around that longitudinal direction while remaining perpendicular to it as if we were (as observer) orbiting in a spy capsule. And the vertical bar of origin would appear unaltered. The time parameter is real, but our choice of measure origin is still observer dependent, unless and only if the wave is a true hydrodynamic surface planar traverse wave. A three dimensional dynamic wave event, whether an air blast or electromagnetic emission would still register a signature as a sinusoid regardless of our position in orbit. Physically the traverse nature of the wave signature is observer dependent and not the total reality.

As to "focusing on the astonishing relations between sinusoidal and exponential functions." that relationship has the form of a hyperbolic function independent of variable parameters. A hyperbola is distinguished as a conical section where the plane is NOT parallel to the slope of the side of the cone, and so the 'legs' of the hyperbola diverge, geometrically. A natural exponential function from which we obtain the base of natural logarithms, can relate to cosine transformations in the rate of change of slope on a sinusoidal curve.

As the observed *N* shape morphs across the time parameter into a bell shape, and a continuous repetition of that bell curve propagates, we observe the sinusoidal wave 'train' of response in our detector which operates as a hyperbolic function. UNLESS!....

...what our detector responds to results in an output of a photoelectric effect! A kinetic, not electromagnetic response. Just as if I were to stroke a pool cue ball to collide with an object ball and the rate of transfer of momentum to the object ball would plot as a ballistic curve, just like the trajectory of a cannonball falling in a gravitational field. And a ballistic curve is a parabolic function, not hyperbolic. A parabola is a conical section where the plane IS parallel to the slope of the side of the cone, and so the 'legs' of the parabola converge towards being parallel with each other. A bell shaped curve cannot evolve to be repeated! AND, while both hyperbolic and parabolic functions have a mathematical identity as *exponential functions*, axiomatically they are not of the same kind. A parabolic function extrapolates from the harmonic series of 2n, and the acceleration of gravity and the half-life of radiological decay are found on the parabolic plane. A hyperbolic function extrapolates from the exponential series of 1+1/n and while plotting close to the harmonic series, has a slightly different rate of change of slope.

So while Fourier Analysis is highly effective in filtering, not 'out' but 'down', to a recognizable wave signal, we are still far from being able to finitely measure a single quanta in an observed wave event. In fact, we really can't say definitely that an electromagnetic emission is a physical wave itself rather than it being a linear projection of energy which is reacted to by detection devices whose inherent energy transfer results in a time dependent rise and fall of induced reactance.

But those are our clues. How is it that an observed kinetic impact (parabolic) can initiate an electromagnetic emission (hyperbolic) such as a piezo-electric oscillator, and an electromagnetic absorption produce a kinetic response. And what determines whether a hyperbolic event, or parabolic event, propagates into yet another of its axiomatic kind, or rotates from a hyperbolic plane onto a parabolic plane, or vise versa.

We are still stuck on Wave-Particle Duality. We must be ignoring something obvious. :-) jrc

Eckard,

to clarify my previous post:

In keeping with your observation of circular symmetry being rarely observerved in nature, while spiral symmetry abounds; that spiral or helical form is observed across a duration in the time parameter. In the 2nd paragraph I failed to specify the "orbital position of the observer" to be on the plane of t=0 throughout the rotation of aspect perpendicular to the longitudinal direction.

By the way, I continue to be impressed with your progress in command of the English language. Kudos, and my humble thanks, you deserve the same from others. respectfully, jrc

Eckard,

"Rob and many others are just focusing on the astonishing relations between sinusoidal and exponential functions." While I do admire the astonishing properties of idealized functions, I have consistently pointed-out, that communications signaling seldom employ such techniques, to recover the information content of signals. They are not useful, precisely because they are so predictable. As Claude Shannon pointed-out long ago, one does not even need to transmit data to another, if that other either already has that data, or can predict it. Information recovery, and hence measurement theory, is all about the acquisition of information that cannot be deduced from what is already known.

Rob McEachern