Semi-fundamental constructs by Eckard Blumschein

Stefan Weckbach's essay challenged me to better explain how I interpret the notions fundamental, frog's view, and causality.

As the title of my essay "semi-fundamental structures" indicates, my boss understood fundamental as do I and as does my dictionary too: "very important or basic" (as is the trunk of a tree structure in comparison with less fundamental branches and roots).

To me existence is not "the most fundamental 'fundamental' one can imagine. This is obvious to me in mathematics, see A infinity and B infinities. Does a real number really exist? Do transfinte cardinalities exist? ...

To me causality, except for Aristotle's fourth case, is most fundamental.

I see his causa finalis due to confusion of the basic Frog's view with the abstracted from it birds view.

Eckard Blumschein

Dear Gordon,

"what is that radical doubt?"

Because the usual notion of time refers to an arbitrarily chosen point t=0 of reference, I doubt that it is an appropriate basis in this case.

This usual scale of time extends from minus infinity to plus infinity and implies therefore the complex Fourier transformation.

Alternatively, the elapsed time refers to something that is non-arbitrary, the actual moment. This scale is always positive, it does permanently slide with respect to the usual scale, and it corresponds to an equivalent real-valued cosine transformation instead FT.

As is obvious since the 1920th but already anchored a decade earlier, QM is based on the usual time scale and accordingly on the redundant complex Fourier view. It doesn't matter whether one prefers Hermitian square matrices or Schroedinger's complex iswave function.

This radicalism of mine is not restricted to QM but it arose from studies of signal processing, in particular of cochlear function.

Eckard

Continuation:

A key discrepance between the usual event-related scale and the object-related scale of elapsed time is an steadily growing phase angle between the two different reference points. In case of calculationof a usual spectrograms, one has to accordingly relocate the origin of the usual time scale again and sgain.

Fröhner mentioned on p. 638 that the wave function is determined only up to a phase factor which is pulled out in his equation (2).

"The superposition principle had been established first as a puzzling empirical feature of the quantum world, before M. Born recognized that the absolute square of the wave function can be interpreted as probability density." The superposition principle corresponds to the Riesz-Fejér theorem.

I guess, cosine transform in IR+ with the natural reference point (elapsed time = 0) is also correct.

Eckard

Corciovei Silviu,

Hacking the brain is not so easy. Va doresc mult success.

Perhaps you feel having understood my essay because you are not aware of contradictory theories which are seemingly fundamental in the sense of mandatory.

You are correct, one may understand "What is fundamental" as a questionable question for a single ultimate fundament of physics.

My boss, you and I understood "fundamental" differently as a pretty universal feature within a logical structure. My metaphore is a tree with many not fundamental roots and many not fundamental branches at its two ends.

Toate Bune,

Eckard

Addendum:

When I was a child who collected stamps I noticed the message "In God we trust".

Weren't Adam and Eve fundamental to everybody? No, at least in this respect, the bible was fundamentally wrong. The same applies for Noah's Arc.

Familiy trees ramify backwards. Just a single male and female individuum are not enough as to cope with occasional genetic defects.

Eckard Blumschein

Gordon Watson wrote:

"Reality makes sense and we can understand it."

In my understanding, this is a tautology because I am merely distinguishing between mysticism and conjectured reality of anything including the also comprehensive notion of the physical universe.

Among the first ones who guided us to get a more fundamental in the sense of comprehensive understanding by consequently excluding mysticism was Lichtenberg (1742-1799),the same professor in Göttingen who coined the notions positive and negative electricity.

His aphorisms include:

- Praying in churches doesn't make the ligthning conductor on them unnecessary.

- God created man to be similar to Him does probably mean, man created God similar to himself.

Eckard Blumschein

A religious believer asked me to further expand on this comment. Well, from the perspective of the 18th century, God is most fundamental. Newton argued:

"God is more important than physics or mathematics. He created the world such as we see it now. Time and space are absolute. Space is the sensorium of God. God winds up the big clock again and again."

Leibniz distinguished three levels of infinity:

- the (currently preferred as mathematical) relative one

- the logically absolute (potential) one

- God as the highest one.

Leibniz criticized the absolute space as too restrictive. He argued, God doesn't need winding up the created by Himself big clock, the universe. On behalf of Newton, Samuel Clark commented: This implies God is redundant, Leibniz is close to atheism.

When I formulated the title of my essay "Semi-fundamental constructs", I was aware of the quite different meaning of the notion semi-fundamental in modern mathematics. With "semi" I rather meant a restriction to a fundament which needn't be straightforward correct but may possibly be of heuristical value.

I anticipate that only people with common sense will be ready to accept that the age of something is more fundamental than its arbitarily attributed location in a human (e.g. Christian) time scale. Please don't mistake this as blasphemy.

Only elapsed time, i.e. the age, can be measured.

Eckard Blumschein

Addendum:

Time is a construct.

Dorogoi Boric Semyonovich,

Perhaps you mistook my utterance "time is (merely) a construct" which means it is semifundanental. I meant, ordinary time is not directly measurable on the tevel of reality. It is based on the truly fundamental elapsed time.

I had two reasons for dealing a bit with what Descartes was teaching in the Netherlands.

At first his speculation about space challenged Guericke to perform experiments instead.

Secondly, Descartes combined ancient geometry with the pretty new use of negative numbers into Cartesian coordinates with extension from minus infinity to plus infinity. Ironically he didn't manage reaching as much freedom as possible because in Cartesioan coordinates one necessarily has to arbitrarily choose a point of reference. Hence, Cartesian coordinates are a mathematically perfect construct while not fundamental to physics.

What about your New Cartesian Physics, I found some interesting claims. However, a more careful scrutiny will take more time. Did you deal with the three belonging experiments (1881, 1889, and 1923) by Michelson?

Eckard Blumschein

Hello Steve,

The word redundant might be a false friend. An Englishman warned me: Don't use it. I means "dismissed by your employer, out of job" (in German arbeitslos).

What I intend to express is something quite different: the property of elements in a mathematical structure that are strictly speaking and with respect to an application unnecessary (= needless) in the sense of avoidable, in principle. Redundant elements increase the apparent volume of information. Hence I consider them and the structure that contains them definitely not fundamental.

This view of mine collides with the also understandable but not always justified strive for more and more generalizing. Several essay authors hope for getting an ultimate fundament of physics by diving "deeper" and deeper. Actually, this strategy leeds to higher and higher levels of abstraction, being as a rule more remote from reality.

What about my ++++, I enjoyed using the symbol box as long as it wasn't misused as to veil the fundamental difference between past and future. Our ancesters were in position to count elapsed days but not future ones. One can only abstract from fundamental observation, not he other way round.

You got my essence. Thank you.

With best regards,

Eckard

Some fundamental (historic) details from Lexikon der Antike:

Jewish time counts from assumed creation of the world at 3761 BC. Greece counted from the first list of winners in panhellenic Olympic games in 776 BC. The Romans started with 753 BC (ab urbe condita). Some Roman provinces each referred to the begin of their Roman rule. Muslims refer to the year of Hedshra 622 AD.

Abbot Dionysius Exiguus suggested referring to anno domini (AD). Carolus Magnus definitely died in 814 AD.

The use of time before the birth of Christ (BC), i.e. negative time, goes back to the French theologian D. Petavius (1583-1652).

Eckard Blumschein