The necessary truth of mathematics (?)

[James R]

But the mathematical dimensionality of Universal relational values and functions can be mapped and AFAIK, constitutes self-evident functional (axiomatic) proof of truth. Example: Gravity.

Word salad. The term "universal relational values" is meaningless. And there's no such thing as an "axiomatic" proof.

 

[Write4U]

Word salad. The term "universal relational values" is meaningless.

Back to semantics again? I did not invent these terms, I merely used them.

Do you understand what I mean to describe in shorthand form? If so, what is the problem?

Universal is self-explanatory
Relational is the way objects relate to and affect each other
Values are the qualities and strengths of the properties that define an object.

Differential equations are formal mathematical expressions of universal relational values.

On the foundations of the universal relation mode​

Abstract​

The universal relation model aims at achieving complete access-path independence in relational databases by relieving the user of the need for logical navigation among relations. We clarify the assumptions underlying it and explore the approaches suggested for implementing it.

The essential idea of the universal relation model is that access paths are embedded in attribute names. Thus attribute names must play unique “roles.” Furthermore, it assumes that for every set of attributes there is a basic relationship that the user has in mind. The user's queries refer to these basic relationships rather than to the underlying database.

Two fundamentally different approaches to the universal relation model have been taken. According to the first approach, the user's view of the database is a universal relation or many universal relations, about which the user poses queries. The second approach sees the model as having query-processing capabilities that relieve the user of the need to specify the logical access path. Thus, while the first approach gives a denotational semantics to query answering, the second approach gives it an operational semantics. We investigate the relationship between these two approaches.

On the foundations of the universal relation model | ACM Transactions on Database Systems

The universal relation model aims at achieving complete access-path independence in relational databases by relieving the user of the need for logical navigation among relations. We clarify the assumptions underlying it and explore the approaches ...

dl.acm.org

​

A simplied universal relation assumption and its properties​

Abstract​

One problem concerning the universal relation assumption is the inability of known methods to obtain a database scheme design in the general case, where the real-world constraints are given by a set of dependencies that includes embedded multivalued dependencies. We propose a simpler method of describing the real world, where constraints are given by functional dependencies and a single join dependency.

The relationship between this method of defining the real world and the classical methods is exposed. We characterize in terms of hypergraphs those multivalued dependencies that are the consequence of a given join dependency. Also characterized in terms of hypergraphs are those join dependencies that are equivalent to a set of multivalued dependencies

https://dl.acm.org/doi/10.1145/319732.319735

Seems that the shorthand term "universal relational values" is a perfectly sound conceptual expression.

And there's no such thing as an "axiomatic" proof.

axiomatic system

In mathematics and logic, an axiomatic system is any set of primitive notions and axioms to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. A formal theory is an axiomatic system (usually formulated within model theory) that describes a set of sentences that is closed under logical implication.[1] A formal proof is a complete rendition of a mathematical proof within a formal system.

Axiomatization​

In mathematics, axiomatization is the process of taking a body of knowledge and working backwards towards its axioms. It is the formulation of a system of statements (i.e. axioms) that relate a number of primitive terms — in order that a consistent body of propositions may be derived deductively from these statements. Thereafter, the proof of any proposition should be, in principle, traceable back to these axioms.

Axiomatic system - Wikipedia

en.wikipedia.org

Seems this is describing "axiomatic proof", no?

 

[exchemist]

Back to semantics again? I did not invent these terms, I merely used them.

Do you understand what I mean to describe in shorthand form? If so, what is the problem?

Universal is self-explanatory
Relational is the way objects relate to and affect each other
Values are the qualities and strengths of the properties that define an object.

Differential equations are formal mathematical expressions of universal relational values.

On the foundations of the universal relation mode​

Abstract​

On the foundations of the universal relation model | ACM Transactions on Database Systems

The universal relation model aims at achieving complete access-path independence in relational databases by relieving the user of the need for logical navigation among relations. We clarify the assumptions underlying it and explore the approaches ...

dl.acm.org

​

A simplied universal relation assumption and its properties​

Abstract​

https://dl.acm.org/doi/10.1145/319732.319735

Seems that the shorthand term "universal relational values" is a perfectly sound conceptual expression.




axiomatic system

Axiomatization​

Axiomatic system - Wikipedia

en.wikipedia.org

Seems this is describing "axiomatic proof", no?

This is idiotic. You are quoting a paper describing a relational database, which tries to be in some sense universal. There is no mention of universal relational values.

It is pathetically obvious that you have, as usual, just gone on the internet and copy-pasted any old shit with these search terms in it, regardless of relevance and without any understanding of what is being referred to.

What useless jerk you are.

 

[Write4U]

This is idiotic. You are quoting a paper describing a relational database, which tries to be in some sense universal. There is no mention of universal relational values.

I had no problem understanding the words in that article.
That article was written by someone with the Association of Computing Machinery. A useless attempt at trying to be universal?
I guess nobody is exempt from your indignance.

What useless jerk you are.

Typical response when there is no valid counter available. Did you understand the meaning of what I posited?
I always thought that communication rested on understanding not on linguistic perfection. Perfection is only required in mathematical expressions. That is why I present only my understanding of the narratives that accompany the scientific symbolics.

You know that science is full of linguistic errors. Scientific terms are not invented by linguists, but by scientists who may be hopelessly lost in the various meanings and definitions of linguistic semantics.
But nobody complained or had a problem interpreting Einstein's use of the non-scientific term "spooky action at a distance". Because he was Einstein!

I have read of medical doctors who had to attend remedial language programs because nobody could even read what they were writing, let alone make sense of their prescriptions. Does that ring a bell?

 

[Write4U]

duplicate.

 

[James R]

Back to semantics again?

Yes. Obviously, since my entire point was that some of the terms you use regularly are literally meaningless.

I did not invent these terms, I merely used them.

You used them in an entirely meaningless way. You fail to communicate anything when you use those terms.

And let's face it: even you don't have a clue what you mean when you use them. It's just filler. Anything to gain a little attention. Anything to provoke a response, even if the reasonable response is "What you just wrote is meaningless nonsense."

Why do you persist?

Do you understand what I mean to describe in shorthand form?

Of course I don't. You fail to communicate anything. Your words literally do not describe anything.

If so, what is the problem?

The problem is that I've been telling you this, on and off, for well over a year now, and yet here you are, still apparently unable to grasp the point, still making lame excuses, still cutting and pasting complete irrelevancies based on random word searches.

This is beyond a joke. What's wrong with you?

Universal is self-explanatory
Relational is the way objects relate to and affect each other
Values are the qualities and strengths of the properties that define an object.

Then "relational values" is an oxymoron. But your attempt to explain is just more filler. The truth is that when you string those three words together in that order, they literally have no meaning.

Differential equations are formal mathematical expressions of universal relational values.

They cannot be, since "universal relational values" is a meaningless term.

---
Then we get your random cut-and-pastes. As exchemist pointed out, you cut and pasted something from somebody talking about relational databases. I guess you just didn't realise, or didn't care. You just googled your words, hoping that somebody else could explain what you meant. It's quite bizarre.

Seems that the shorthand term "universal relational values" is a perfectly sound conceptual expression.

In the specific context of relational databases, you mean? Something that you were not even trying to talk about?

Who do you think you're fooling? Are you fooling yourself?

 

[James R]

I had no problem understanding the words in that article.

This is idiotic. Words are meant to communicate something. Sure, you understand at some level that individual words have meanings. But you obviously have zero understanding of what the article you googled is about. I doubt you give a damn.

That article was written by someone with the Association of Computing Machinery. A useless attempt at trying to be universal?

Don't try to palm off your own failure onto other people. You clearly don't have a clue what that somebody from the Association of Computing Machinery was writing about. And even if you did, that content has no relevance to your previous stringing together of the words "universal", "relational" and "value".

I guess nobody is exempt from your indignance.

Wake up, Write4U! We're criticising you here, not somebody else. Two wrongs don't make a right. Somebody else being clueless at some other time in some other place doesn't excuse your wilful cluelessness here and now.

Did you understand the meaning of what I posited?

It was, quite literally, meaningless. Just like all the other times you've used those words in that order.

That is why I present only my understanding of the narratives that accompany the scientific symbolics.

You make stuff up and then when you're called out on your bullshit you try to google up some excuses.

You know that science is full of linguistic errors.

Like what?

Scientific terms are not invented by linguists, but by scientists who may be hopelessly lost in the various meanings and definitions of linguistic semantics.

Scientists generally manage to communicate something when they communicate. You, on the other hand, seem to have to constantly try to make up excuses after the fact for the nonsense you post.

But nobody complained or had a problem interpreting Einstein's use of the non-scientific term "spooky action at a distance". Because he was Einstein!

No. It was because Einstein was a good communicator. He explained himself. He knew what he wanted to say and when he said or wrote something the meaning was usually clear. He made an effort.

I have read of medical doctors who had to attend remedial language programs because nobody could even read what they were writing, let alone make sense of their prescriptions. Does that ring a bell?

Are you saying that you think you need to attend remedial language programs, or that you have done so already?

 

[Write4U]

This is idiotic. Words are meant to communicate something. Sure, you understand at some level that individual words have meanings. But you obviously have zero understanding of what the article you googled is about. I doubt you give a damn.

I have the ability to see underlying principles in disparate conditions. Do you truly understand the word "gestalt" used in science and literature.

What is gestalt in simple terms?
The word Gestalt is used in modern German to mean the way a thing has been “placed,” or “put together.”
There is no exact equivalent in English. “Form” and “shape” are the usual translations; in psychology the word is often interpreted as “pattern” or “configuration.”

Gestalt psychology | Definition, Founder, Principles, & Examples | Britannica

Gestalt psychology, school of psychology founded in the 20th century that provided the foundation for the modern study of perception. Gestalt theory emphasizes that the whole of anything is greater than its parts. That is, the attributes of the whole are not deducible from analysis of the parts...

www.britannica.com

and/or

What is the meaning of Gestalt in science?: a structure, arrangement, or pattern of physical, biological, or psychological phenomena so integrated as to constitute a functional unit with properties not derivable by summation of its parts. Sep 14, 2024

Definition of GESTALT

something that is made of many parts and yet is somehow more than or different from the combination of its parts; broadly : the general quality or character of something… See the full definition

www.merriam-webster.com

Take your pick.

Gestalt psychology

Theoretical framework and methodology​

The Gestalt psychologists practiced a set of theoretical and methodological principles that attempted to redefine the approach to psychological research. This is in contrast to investigations developed at the beginning of the 20th century, based on traditional scientific methodology, which divided the object of study into a set of elements that could be analyzed separately with the objective of reducing the complexity of this object.

The principle of totality asserts that conscious experience must be considered globally by taking into account all the physical and mental aspects of the individual simultaneously, because the nature of the mind demands that each component be considered as part of a system of dynamic relationships. Thus, holism as fundamental aspect of Gestalt psychology.[9][24]

Moreover, the perception of the nature of a part depends upon the whole in which it is embedded.[9][25] The maxim that the whole is more than the sum of its parts is not a precise description of the Gestaltist view.[9] Rather, as Koffka writes, "The whole is something else than the sum of its parts, because summing is a meaningless procedure, whereas the whole-part relationship is meaningful."[26]

"The whole is greater than the sum of its parts".

Principles

The Gestaltists were the first to document and demonstrate empirically many facts about perception—including facts about the perception of movement, the perception of contour, perceptual constancy, and perceptual illusions.[14] Wertheimer's discovery of the phi phenomenon is one example of such a contribution.[28]

Properties​

The key principles of gestalt systems are emergence, reification, multistability and invariance.[29] These principles are not necessarily separable modules to model individually, but they could be different aspects of a single unified dynamic mechanism.[30]

Perceptual grouping

Like figure-ground organization, perceptual grouping (sometimes called perceptual segregation)[31] is a form of perceptual organization.[16] Perceptual grouping is the process that determines how organisms perceive some parts of their perceptual fields as being more related than others,[16] using such information for object detection.[31]

Problem solving and insight

Gestalt psychology contributed to the scientific study of problem solving.[28] In fact, the early experimental work of the Gestaltists in Germany[note 2] marks the beginning of the scientific study of problem solving. Later this experimental work continued through the 1960s and early 1970s with research conducted on relatively simple laboratory tasks of problem solving.[note 3][43]

Gestalt psychology - Wikipedia

en.wikipedia.org

And this is why I am enchanted with mathematics. It is the Gestalt of the Universe

Gestalt Mathematics​

Attention to the actual names by which phenomena are called reflects the Gestalt process itself, although not all practitioners of Gestalt are willing to carry it that far. The etymologies are histories of consciousness, and show how the patterns we create have developed and intermingled. In discussing the relation of the discrete to the continuous, the words we use represent the boundaries we set, which we cannot see from both aides without considering the formal properties of language as well as the semantic.

Transcendentalist Emerson saw a word as a "fossil poem." The sounds of the words we utter affect our experience directly, a fact once recognized in the sense of sacred speech and implicit in the notion of a mantram. The shapes of the letters we use to represent the words undergo iconic processing in the brain in parallel with the symbolic exercise of "reading." In the forms used to express Gestalt we may see a general theory.

Gestalt Mathematics — Kurt von Meier

“The contribution of the Gestalt approach is the recognition that figure and ground are formally the same and may be exchanged without violence to the whole, and in fact must be changed for a complete experience of the whole. When we understand something, we stand under it, experience it fr

www.kurtvonmeier.com

 

[James R]

I have the ability to see underlying principles in disparate conditions.

Good for you.

Do you truly understand the word "gestalt" used in science and literature.

Is that what we've been talking about? Err... no, I don't think it is.

Are we about to see another random cut-and-paste session from the internet? I think so.

And this is why I am enchanted with mathematics. It is the Gestalt of the Universe

Again, good for you.

Did you consider anything I wrote in my most recent posts to you?

 

[Write4U]

Did you consider anything I wrote in my most recent posts to you?

Why? If you make no effort to even try to follow what it is I am trying to say, why bother?

 

[quant]

The Universe knows only one UNIVERSAL mathematical language where the symbolic representation of 2 + 2 = 4, logically, always, everywhere.

But once imaginary numbers are introduced, all that goes out of the window. I am sure most mathematicians would agree that introducing imaginary numbers into calculations is not comparable to pure mathematics and yields contestable results.

 

[Write4U]

But once imaginary numbers are introduced, all that goes out of the window. I am sure most mathematicians would agree that introducing imaginary numbers into calculations is not comparable to pure mathematics and yields contestable results.

That is true for human symbolic mathematics. But I am not discussing human maths. That is all theoretical (abstract)

The Universe doesn't deal with symbolic numbers, it deals mathematically with "relational values" and logical "differential equations". Gestalt!
Hence Einstein's "Theory of Relativity"" uses the term "relativity" to identify the relational properties and functions in Universal mechanics.

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives.[1] In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. https://en.wikipedia.org/wiki/Differential_equation

It is also used by the Universe itself in a generic manner.
The universe does not describe itself. Its observable mathematical (interactive) functions can be symbolically described by human mathematics.

The reason why human maths is "unreasonably effective" is because it is derived and codified from the observation of the way matter and forces in nature (the universe) act relationally (relative to each other).

This may sound simplistic, but AFAIK mathematics is the only "human language" that is derived from observation of nature.

A mathematical equation in physics is a statement, and that statement represents a physical fact (or it does not if it happens to be wrong.)

Human maths can be wrong, but Universal maths are never wrong.

 

[exchemist]

But once imaginary numbers are introduced, all that goes out of the window. I am sure most mathematicians would agree that introducing imaginary numbers into calculations is not comparable to pure mathematics and yields contestable results.

Don’t be silly. Complex numbers have been an integral part of pure mathematics for centuries. There is nothing remotely “contestable” about them. For example de Moivre’s theorem and Euler’s representation of complex numbers were both developed in the c.18th. The term “imaginary”, for the component multiplied by i ( = √-1), had already been introduced by Descartes in the c.17th - though he applied it to the whole number rather than just what we now call the imaginary part. And Argand, of the eponymous diagram for representing them graphically, developed his idea at the start of the c.19th.

Complex numbers are taught in 6th Form pure mathematics courses in schools all over the world.

 

[James R]

Why? If you make no effort to even try to follow what it is I am trying to say, why bother?

So, that's a "no", then.

Why should I bother with you?

 

[James R]

That is true for human symbolic mathematics. But I am not discussing human maths. That is all theoretical (abstract)

There's no other kind of maths available.

The Universe doesn't deal with symbolic numbers, it deals mathematically with "relational values" and logical "differential equations". Gestalt!

I haven't seen anything in the universe doing differential equations, apart from human beings. Have you?

Hence Einstein's "Theory of Relativity"" uses the term "relativity" to identify the relational properties and functions in Universal mechanics.

There is no "Hence". What you wrote doesn't follow.

It is also used by the Universe itself in a generic manner.

"Generic manner"? Meaningless word salad.

The universe does not describe itself.

Indeed.

Its observable mathematical (interactive) functions can be symbolically described by human mathematics.

Where and how can we see the universe's observable mathematical interactive functions?

The reason why human maths is "unreasonably effective" is because it is derived and codified from the observation of the way matter and forces in nature (the universe) act relationally (relative to each other).

You have said nothing that explains the mystery of the effectiveness of mathematics. All you have said is that humans use mathematical models, which is true but unhelpful if your concern is with the mystery.

This may sound simplistic, but AFAIK mathematics is the only "human language" that is derived from observation of nature.

A very large amount of mathematics is not derived from the observation of nature. It is pure concept, built out of abstract axioms and such. "Derived" is also a terrible word to use, there. When a mathematician derives a mathematical proof, she does not pay any attention to observations of nature. That would be science, not maths.

Human maths can be wrong, but Universal maths are never wrong.

Word salad. "Universal maths" is just something you made up. It alludes to something, but when you talk about it it's an empty concept.

 

[Write4U]

There's no other kind of maths available.

The Universe operated mathematically before humans symbolized it. We did not invent maths. We codified it.

I haven't seen anything in the universe doing differential equations, apart from human beings. Have you?

Every observable action is an expressed differential equation.

What will change when we take humans out of the equation? Nothing will change.

A "deterministic event" is what we have symbolized as an expressed "linear differential equation"

Classifying Differential Equations​

When you study differential equations, it is kind of like botany. You learn to look at an equation and classify it into a certain group. The reason is that the techniques for solving differential equations are common to these various classification groups. And sometimes you can transform an equation of one type into an equivalent equation of another type, so that you can use easier solution techniques. Here then are some of the major classifications of differential equations:

Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form

Linear just means that the variable in an equation appears only with a power of one. So x is linear but x2 is non-linear. Also any function like cos(x) is non-linear.

Linear vs. Non-linear

In math and physics, linear generally means "simple" and non-linear means "complicated". The theory for solving linear equations is very well developed because linear equations are simple enough to be solveable. Non-linear equations can usually not be solved exactly and are the subject of much on-going research. Here is a brief description of how to recognize a linear equation.

In math and physics, linear generally means "simple" and non-linear means "complicated". The theory for solving linear equations is very well developed because linear equations are simple enough to be solveable. Non-linear equations can usually not be solved exactly and are the subject of much on-going research. Here is a brief description of how to recognize a linear equation.
where m, b are constants ( m is the slope, and b is the y -intercept). In a differential equation, when the variables and their derivatives are only multiplied by constants, then the equation is linear. The variables and their derivatives must always appear as a simple first power.

A partial differential equation (or PDE) has an infinite set of variables which correspond to all the positions on a line or a surface or a region of space. For example in the string simulation we have a continuous set of variables along the string corresponding to the displacement of the string at each position. In practice we approximate the infinite set of variables with a finite set of variables spread across the string (or surface or volume) at each position.

myPhysicsLab Classifying Differential Equations

www.myphysicslab.com

 

[Write4U]

There is no "Hence". What you wrote doesn't follow.

Einstein recognized the "variable relationships" between physical objects. Hence the term "relativity".

"Generic manner"? Meaningless word salad.

Generic to Universal constants.

p.s. a word salad is an expressed differential equation...

 

[exchemist]

Einstein recognized the "variable relationships" between physical objects. Hence the term "relativity".

Generic to Universal constants.

p.s. a word salad is an expressed differential equation...

No, the other way round: "expressed differential equation" is word salad.

 

[Write4U]

Where and how can we see the universe's observable mathematical interactive functions?

Fractals

You have said nothing that explains the mystery of the effectiveness of mathematics. All you have said is that humans use mathematical models, which is true but unhelpful if your concern is with the mystery.

But you don't understand. The human effectiveness of its symbolic mathematics is descriptive of the logical effectiveness of expressed natural (universal) mathematical functions.

 

[Write4U]

No, the other way round: "expressed differential equation" is word salad.

All compound sentences are word salads. The "differences" (equations expressed in reality) lie in the combined kinds and flavors...
Patterns within chaos.