Write4U's wobbly world of word salad woo

[exchemist]

Shrugs.
Sorry, I don't agree with that narrow perspective.

Are you telling me that these people are wrong?

The Neurodynamics of Cognition: A Tutorial on Computational Cognitive Neuroscience

2. A brief history​

The Neurodynamics of Cognition: A Tutorial on Computational Cognitive Neuroscience - PMC

Computational Cognitive Neuroscience (CCN) is a new field that lies at the intersection of computational neuroscience, machine learning, and neural network theory (i.e., connectionism). The ideal CCN model should not make any assumptions that are ...

pmc.ncbi.nlm.nih.gov

Are "partial differential equations" not a form of "differential equation"?

What a stupid question. Partial differential equations fit within the description I linked to in post 495. If you had an atom of understanding of mathematics, you would realise this. The clue is even in the name. Durrh.

 

[Write4U]

Humans sometimes use mathematics to model physical behaviours, certainly.

You mean that humans model "natural occurrences"?

Did you notice the words "In mathematics"? Big hint, there!

Did you notice the words "dimension of a manifold"? Seems like a Big hint there also.
You are still anthropomorphizing!

Generic mathematics are a property of spacetime. The dimension of time is an abstract mathematical object. No atoms to found in the dimension of time. Hence the term "Temporal", not "Spatial".

Spacetime​

In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three (physical) dimensions of space and the one (temporal) dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.

Spacetime - Wikipedia

en.wikipedia.org

(bracketed mine)

 

[Write4U]

What a stupid question. Partial differential equations fit within the description I linked to in post 495. If you had an atom of understanding of mathematics, you would relise this.

WOW, did I say you were wrong? Recheck my post # 500, please. I just added a link to 6 more non-atomic examples of DE.

 

[exchemist]

WOW, did I say you were wrong? Recheck my post # 500, please.

It is a stupid question.

 

[Write4U]

It is a stupid question.

Are you chiding me for a wrong question or a wrong statement? This is getting bizarre.
Good day, sir (good night for me)

 

[Write4U]

Recognised it? We invented it.

No we did not. We symbolized it ....difference! Mathematical values and processes was there all along. We discovered and codified it.

Can't symbolize something that does not exist . That's religion!

Prayer (religious modeling) does not produce results, because that's not how it works. Physics (mathematical modeling) does produce results, because that is how it works.

Spacetime​

In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events occur.

Spacetime - Wikipedia

en.wikipedia.org

Everything within the mathematical model is governed by mathematics of the modeled spacetime manifold geometry.
A functional model is proof of truth by its succesful results upon execution.
The mathematical model of how to physically produce the Higgs boson, did in fact produce the boson, proving the accuracy and effectiveness of the mathematical model.

Without the "sufficient" presence of the "necessary" values, the event does not physically materialize. So it is in a lab, so it is in spacetime.

 

[James R]

Write4U:

Once again, typically and predictably, you have cherry picked one or two lines from the three careful and detailed responses I wrote to you. And, again, you have completely and miserably failed yet again to address the main problem with your assertions about mathematics, which I carefully walked you through for the umpteenth time.

This discussion is a complete waste of my time. I don't think you're paddling with all oars in the water. I don't know whether you realise that, or not.

 

[Write4U]

Write4U:

Once again, typically and predictably, you have cherry picked one or two lines from the three careful and detailed responses I wrote to you. And, again, you have completely and miserably failed yet again to address the main problem with your assertions about mathematics, which I carefully walked you through for the umpteenth time.

This discussion is a complete waste of my time. I don't think you're paddling with all oars in the water. I don't know whether you realise that, or not.

OK, you just keep using mathematics to probe the mysteries of the universe, because they are just a fanciful invention from the human mind but have no connection with reality.
Apparently Archimedes, Pythagoras, Plato, Gallileo, Leibniz, Wittgenstein, Kepler, Newton, Bacon, the brilliant minds that studied and explained the mathematical behaviors of the universe. The very inventors of human mathematics had no paddle in the water at all? And you know better?

ccontiued..

 

[Write4U]

...continued

Mathematics: The Beautiful Language of the Universe
JUNE 6, 2015 BY JOSHUA CARROLL

Let us discuss the very nature of the cosmos. What you may find in this discussion is not what you expect. Going into a conversation about the universe as a whole, you would imagine a story full of wondrous events such as stellar collapse, galactic collisions, strange occurrences with particles, and even cataclysmic eruptions of energy. You may be expecting a story stretching the breadth of time as we understand it, starting from the Big Bang and landing you here, your eyes soaking in the photons being emitted from your screen.

Of course, the story is grand. But there is an additional side to this amazing assortment of events that oftentimes is overlooked; that is until you truly attempt to understand what is going on. Behind all of those fantastic realizations, there is a mechanism at work that allows for us to discover all that you enjoy learning about. That mechanism is mathematics, and without it the universe would still be shrouded in darkness.

In this article, I will attempt to persuade you that math isn’t some arbitrary and sometimes pointless mental task that society makes it out to be, and instead show you that it is a language we use to communicate with the stars.

Mathematics: The Beautiful Language of the Universe

Let us discuss the very nature of the cosmos. What you may find in this discussion is not what you expect. Going into a conversation about the universe as a whole, you would imagine a story full of wondrous events such as stellar collapse, galactic collisions, strange occurrences with particles...

www.universetoday.com

Is nature mathematical?
By Paul Davies

Scientists do not use mathematics merely as a convenient way of organising the data. They believe that mathematical relationships reflect real aspects of the physical world. Science relies on the assumption that we live in an ordered Universe that is subject to precise mathematical laws. Thus the laws of physics, the most fundamental of the sciences, are all expressed as mathematical equations. Working physicists adopt a quantitative approach to almost all investigations, and physics tends to be taken as a model for how any successful science should be formulated.

more... https://www.newscientist.com/article/mg13318134-400-is-nature-mathematical/

Relationship between mathematics and physics​

Historical interplay​

Before giving a mathematical proof for the formula for the volume of a sphere, Archimedes used physical reasoning to discover the solution (imagining the balancing of bodies on a scale).[11] Aristotle classified physics and mathematics as theoretical sciences, in contrast to practical sciences (like ethics or politics) and to productive sciences (like medicine or botany).[12]

From the seventeenth century, many of the most important advances in mathematics appeared motivated by the study of physics, and this continued in the following centuries (although in the nineteenth century mathematics started to become increasingly independent from physics).[13][14] The creation and development of calculus were strongly linked to the needs of physics:[15]

There was a need for a new mathematical language to deal with the new dynamics that had arisen from the work of scholars such as Galileo Galilei and Isaac Newton.[16] The concept of derivative was needed, Newton did not have the modern concept of limits, and instead employed infinitesimals, which lacked a rigorous foundation at that time.[17] During this period there was little distinction between physics and mathematics;[18] as an example, Newton regarded geometry as a branch of mechanics.[19]

According to David Hume, only statements that deal solely with ideas themselves—such as those encountered in mathematics—can be demonstrated to be true with certainty, while any conclusions pertaining to experiences of the real world can only be achieved via "probable reasoning".[29]

IMO, the eason for that is the dynamical nature of the universe. If the universe was not dynamical, it would be mathematically perfect.

This leads to a situation that was put by Albert Einstein as "No number of experiments can prove me right; a single experiment can prove me wrong."[30] The ultimate goal in research in pure mathematics are rigorous proofs, while in physics heuristic arguments may sometimes suffice in leading-edge research.[31] In short, the methods and goals of physicists and mathematicians are different.[32] Nonetheless, according to Roland Omnès, the axioms of mathematics are not mere conventions, but have physical origins.[33]

Role of rigor in physics​

See also: Theoretical physics and Mathematical physics
Rigor is indispensable in pure mathematics.[34] But many definitions and arguments found in the physics literature involve concepts and ideas that are not up to the standards of rigor in mathematics.[31][35][36][37]

Relationship between mathematics and physics - Wikipedia

en.wikipedia.org

IMO, all this confirms the fundamental mathematical nature of physical behaviors and expressions. I see no flaw in that argument.

 

[TheVat]

The mathematical model of how to physically produce the Higgs boson, did in fact produce the boson, proving the accuracy and effectiveness of the mathematical model

Notice the word "model" that keeps appearing there. A model is a description, in this case employing the language of math, which proves to be empirically adequate as a description. The physical universe is not its description, the map is not the territory.

Scientists do not use mathematics merely as a convenient way of organising the data. They believe that mathematical relationships reflect real aspects of the physical world. Science relies on the assumption that we live in an ordered Universe that is subject to precise mathematical laws. Thus the laws of physics, the most fundamental of the sciences, are all expressed as mathematical equations.

Notice the wording carefully. Math reflects aspects of the physical. It's an abstract way to represent the physical. While Davies can say the universe "is subject to precise mathematical laws," one can just as well say that our math models (laws) are subject to the empirically accessible universe, one which is accessible at all because it is ordered and shows a type of uniformity. The chaotic universes could be out there, but they don't support any life which could observe them as chaotic.

 

[Write4U]

The physical universe is not its description, the map is not the territor

I understand that. But a mathematical description of all the physical properties of that hill informs the climber exactly what tools are required to climb that hill. To pysically describe the hill without mathematics leaves the climber with the fact of an "unknown" quantity and quality of the territory.
The hill would be just a "hill", and that is only in the English language.

A rock rolling down the "slope" of the hill does not need to know the mathematics of gravity or friction. The people living at the bottom of the hill do.
Human symbolized mathematics are not part of the universe. They are just symbolic representations, but what they represent is a real part of the universe.

The map represents the terrain in human "language". But if correctly done it quantifies and qualifies the terrain as it is in nature.

Without the map the explorer is blind. Without the mathematical description of anything it just remains a "thing" instead of a "known" quantity.
As was observed before , wihout mathematics we'd still be in scientific "dark ages". The reason is that mathematics adequately, if not exactly describe the relational values and functions that are employed by the universe itself. IMO, there is nothing wrong with the concept of a mathematically functioning universe.

I am not talking about the number 2 floating about in space, but that number adequately maps the location of 2 interactive objects at any given mathematical point in space.

The very fact that the unmapped parts of nature are the "unknown" parts, proves the efficacy of the parts that can be mapped and are amenable to accurate descriptive quantification.
Human maths map and represent natural (generic) maths in a symbolic fashion. I don't see any problem with that concept.

The physical world functions in accordance with natural mathematical principles. That's why the representative physical sciences rely on symbolic representative mathematics. Is that not a logical conclusion?

 

[Pinball1970]

The physical world functions in accordance with natural mathematical principles. That's why the representative physical sciences rely on symbolic representative mathematics. Is that not a logical conclusion?

No

 

[Pinball1970]

A rock rolling down the "slope" of the hill does not need to know the mathematics of gravity or friction. The people living at the bottom of the hill do.

What?

 

[Pinball1970]

But a mathematical description of all the physical properties of that hill informs the climber exactly what tools are required to climb that hill.

So what? Wordsworth did the same.

 

[Write4U]

What?

Would you want to know if that rock was stable or unbalanced and if it fell how far it would roll based on the maths?

So what? Wordsworth did the same.

I doubt that very much. Poetry does not solve a differential equation. Mathematics does.
The "Law of falling bodies" is a symbolized mathematical expression of real world dynamics and is predictive of the actual physics.


p.s. the climber was a poor example. A rock rolling downhill is more illustrative of the "terrain".

 

[Write4U]

W4U said:
The physical world functions in accordance with natural mathematical principles. That's why the representative physical sciences rely on symbolic representative mathematics. Is that not a logical conclusion?

No

Prove it wrong.
Why do all sciences worldwide use mathematics as the only universally acceptable language, unless mathematics is the only known language that accurately describes universal values and functions and can be used to accurately predict and/or create future events. That alone speaks for itself.

 

[Pinball1970]

solve a differential equation

When you have you ever solved one of those?

 

[Pinball1970]

functions

You don't know what that means either.

I'm done. I think I put in a decent knock? My scoring has been slow but most of the deliveries have been repeated wides.
Run out due to extreme fatigue.

 

[Write4U]

When you have you ever solved one of those?

Everyone uses them all day long. It is part of every day life. It is an evolved survival mechanism.

Differential Equation Systems and Nature
August 27, 2023/12 Comments/in Bio/Chem Articles, Mathematics Articles

Abstract

“Mathematics is the native language of nature.” is a phrase that is often used when it comes to explaining why mathematics is all around in natural sciences, especially in physics. What does that mean?

A closer look shows us that it primarily means that we describe nature by differential equations, a lot of differential equations. There are so many that it would take an entire encyclopedia to gather all of them in one book. The following article is intended to take the reader through this maze along with examples, many pictures, a little bit of history, and the theorem about the existence and uniqueness of solutions: the theorem of Picard-Lindelöf.

Reference: https://www.physicsforums.com/insights/differential-equation-systems-and-nature/

 

[Write4U]

You don't know what that means either.

I'm done. I think I put in a decent knock? My scoring has been slow but most of the deliveries have been repeated wides.
Run out due to extreme fatigue.

OK, thank you for making me work. It seems that I have been using the term "differential equation" not quite in accurately, but not necessarily completetely wrong either.

From now on I shall use the term "difference equation" as that more accurately defines my meaning in context.

Difference Equation​

---

A difference equation, also called a finite difference equations, is an equation that involves finite differences of a function.
Difference equations are the finite analogs of differential equations.

Difference Equation -- from Wolfram MathWorld

A difference equation, also called a finite difference equations, is an equation that involves finite differences of a function. Difference equations are the finite analogs of differential equations.

mathworld.wolfram.com

and here,

7 — DIFFERENCE EQUATIONS

Many problems in Probability give rise to difference equations. Difference equations relateto differential equations as discrete mathematics relates to continuous mathematics.Anyone who has made a study of differential equations will know that even supposedlyelementary examples can be hard to solve. By contrast, elementary difference equationsare relatively easy to deal with.

Aside from Probability, Computer Scientists take an interest in difference equations for anumber of reasons. For example, difference equations frequently arise when determiningthe cost of an algorithm in big-O notation. Since difference equations are readily handledby program, a standard approach to solving a nasty differential equation is to convert itto an approximately equivalent difference equation

more... https://www.cl.cam.ac.uk/teaching/2003/Probability/prob07.pdf