The Language of Physics.

[Write4U]

No such animal

The Nature of Mathematics
(These paragraphs are reprinted with permission from Everybody Counts: A Report to the Nation on the Future of Mathematics Education. ©1989 by the National Academy of Sciences. Courtesy of the National Academy Press, Washington, D.C.)

Mathematics reveals hidden patterns that help us understand the world around us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems.

As a practical matter, mathematics is a science of pattern and order. Its domain is not molecules or cells, but numbers, chance, form, algorithms, and change. As a science of abstract objects, mathematics relies on logic rather than on observation as its standard of truth, yet employs observation, simulation, and even experimentation as means of discovering truth.

The special role of mathematics in education is a consequence of its universal applicability. The results of mathematics--theorems and theories--are both significant and useful; the best results are also elegant and deep. Through its theorems, mathematics offers science both a foundation of truth and a standard of certainty.

In addition to theorems and theories, mathematics offers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols. Experience with mathematical modes of thought builds mathematical power--a capacity of mind of increasing value in this technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to suggest alternatives. Mathematics empowers us to understand better the information-laden world in which we live.

https://services.math.duke.edu/undergraduate/Handbook96_97/node5.html

"The Universe does not have "some" mathematical properties, it has "only" mathematical properties" (Tegmark)

 

[Michael 345]

The Nature of Mathematics

A lengthy description of mathematics ✓

Human mathematics ✓

Before we invented mathematics there was stuff. Stuff did not employ math. It just existed

Natural mathematics? No such animal

 

[Write4U]

A lengthy description of mathematics ✓

Human mathematics ✓

Before we invented mathematics there was stuff. Stuff did not employ math. It just existed

Natural mathematics? No such animal

Just stuff? You cannot see the expressed mathematical orders in these examples ?

fractals in nature. snail shell // milky way // leaf veins // motor neuron

No matter where we look in the natural world, we are sure to find recurring patterns. As a result, natural scientists devote their careers to [humbly] attempt to find and define these very patterns. The most abundant of these natural motifs is arguably the fractal—a geometric structure that can be subdivided into smaller parts that look roughly similar to the whole. Take the branching pattern of the veins on a leaf as an example: zoom into one of those branches, and you’ll find that it’s reminiscent of the overarching branching structure // zoom into one of those branches’ branches and you’ll find the same thing… over and over again!

At their core, fractals are simply the geometric result of repeating the same pattern over and over at a smaller and smaller scale—increasingly tiny patterns within a greater overarching motif. But fractals are the ultimate paradox. Though they are built on simple repetitions, they are infinitely complex. You can subdivide // zoom in // subdivide // zoom in and you’ll still see the same [or similar] patterns emerging and repeating with detail at all scales. Nature is built on these repetitions, all the way down to the subatomic level—the quarks // leptons // bosons.1

“Philosophy is … written in the language of mathematics, and its characters are triangles, circles, and other geometric figures … without these, one is wandering about in a dark labyrinth.” —Galileo Galilei

The ultimate quest for a mathematician is to define simple equations with far-reaching consequences: a2 + b2 = c2 // eiπ + 1 = 0 // E=mc2. The aim is to distill limitless complexity down into elegant and powerful formulas. Surprisingly, despite the natural abundance of the fractal form, it was not until the 20th century that mathematicians even really began investigating fractal structures and their geometry. In fact, it was not even until 1975 that mathematician Benoît Mandelbrot even gave a name to these forms! Mandelbrot is largely credited with elevating the study of fractals to its prominence today, beginning with his discovery of the Mandelbrot set.2

Forever zooming in.

Mandelbrot created his revolutionary // revelationary set essentially by assigning every point on a screen with a unique number. He then plugged each number into a formula, got a result, and plugged the result back into the formula.3 Over and over. Millions and billions of times. In this manner, Mandelbrot tracked the fate of each point on the screen; either it grew to infinity or shrank to zero through these repetitions. If the initial number shrank—was bounded— he colored the point black. If, however, it grew—or escaped—to infinity, he assigned the point a particular color based on how many times he could repeat the formula before the result became exceedingly large.

“I never had the feeling that my imagination was rich enough to invent all those extraordinary things … They were there, even though nobody had seen them before. It’s marvelous … the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science.” —Benoît Mandelbrot
http://incubator.rockefeller.edu/fractaled-atlas/

​

 

[Michael 345]

Just stuff?

Yep, pretty photos of stuff, but ultimately just stuff

Of course humans can wax lyrical about stuff, and stir the loins and emotions of others, can even observe, prod, poke, even shrink wrap mathematics around it

Some even worship stuff

Ultimately stuff remains stuff. We vanish from the Universe, stuff remains. We can manipulate stuff and change it into other forms of stuff, no matter, stuff is stuff

Do you have trouble with stuff being stuff?

I admit calling everything stuff when another person wants a particular type of stuff is not helpful but who said stuff needed to be helpful

This lump of stuff is going to get some light brown stuff in a container of stuff to drink

Translate - coffee moment

 

[Write4U]

It just existed

If stuff did not have a value it would not exist as stuff. It would be meta-stuff.....

Do you have trouble with stuff being stuff?

No, as long as the stuff has a relational values that makes interaction with other stuff in a specific way possible...

 

[Michael 345]

If stuff did not have a value it would not exist as stuff. It would be meta-stuff.....

No, as long as the stuff has a relational values that makes interaction with other stuff in a specific way possible...

Noooooo it has physics to make interactions

If human stuff feel the need to use stuff to inscribe squiggles on other stuff noting the interactions this lumb of stuff says no problem

Want to call squigged stuff on other stuff mathematics? Sure go ahead

 

[Write4U]

Noooooo it has physics to make interactions

I disagree. Stuff has interactive values, not interactive physics. That is a meaningless term.

IMO physics describes "existense of evolutionary continuance". Mathematics describe the values and functions by which it "self-organizes it's continued existence". Logic demands a value system by which reality may be relationally measured.

Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid-19th century). More recently, logic has been studied in cognitive science, which draws on computer science,
linguistics, philosophy and psychology, among other disciplines. A logician is any person, often a philosopher or mathematician, whose topic of scholarly study is logic.

Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only imaginary. The term is also used to refer to the ontological status of things, indicating their existence.[1] In physical terms, reality is the totality of a system, known and unknown.[2]

Philosophical questions about the nature of reality or existence or being are considered under the rubric of ontology, which is a major branch of metaphysics in the Western philosophical tradition. Ontological questions also feature in diverse branches of philosophy, including the philosophy of science,
philosophy of religion, philosophy of mathematics, and philosophical logic.

These include questions about whether only physical objects are real (i.e., Physicalism), whether reality is fundamentally immaterial (e.g., Idealism), whether hypothetical unobservable entities posited by scientific theories exist, whether God exists, whether numbers and other abstract objects exist, and whether possible worlds exist.

I believe that mathematics is the informational language of physics and physical existence.
I guess, that makes me an Idealist....

 

[Michael 345]

I believe that mathematics is the informational language of physics and physical existence.

Do you consider math to be discovered or invented?

 

[Write4U]

Do you consider math to be discovered or invented?

Both,

"Natura Artis Magistra" = Nature is the teacher of arts (sciences).

By most accounts, generic natural (logical) mathematics are discovered.
(a + b = c) = universal logical constant.

The Fibonacci Sequence is a universal logical constant. (a + b = c + b = d + c = e + d = f + ......)

By all accounts, symbolic human maths are invented.
(one plus two = three) = (1 + 2 = 3) = (I + II = III) = arbitrary human symbolic mathematical representations of universal logical constants.

Patterns in nature

Patterns in nature are visible regularities of form found in the natural world. These patterns recur in different contexts and can sometimes be modelled mathematically. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes.[1]

Early Greek philosophers studied pattern, with Plato, Pythagoras and Empedocles attempting to explain order in nature. The modern understanding of visible patterns developed gradually over time.

https://en.wikipedia.org/wiki/Patterns_in_nature

Examples of patterns in nature

Examples of patterns in nature, including the golden spiral, the golden ratio and fractal self-similar structures. From left to right, (a) a nautilus shell, a galaxy, a sunflower, a desert plant; (b) a storm formation, a fern bud, an ocean wave, a finger print; (c) fractal properties in a branched tree, a leaf, river bed formation, a cast of human lungs.

https://www.researchgate.net/figure...l-the-golden-ratio-and-fractal_fig2_330531039

Abstraction in Mathematics Learning
Synonyms : Abstract representation; Mental abstraction; Metaknowledge

Definitions

Mathematical objects include concepts, relationships, structures, and processes. In mathematics learning, the term abstraction is used in two senses: An abstraction is a mental representation of a mathematical object.

Abstraction, without an article, is the mental process by which an individual constructs such an abstraction. The term derives from the Latin abstractum, literally “drawn out.”

Abstraction in mathematics learning takes many forms. At the most elementary level, called empirical abstraction, learners recognize that some objects, situations, or experiences are similar in a particular way that distinguishes them from others. The essence of this similarity is then drawn out to form a mental object in its own right. In horizontal mathematization, symbols are used to create a mathematical object that expresses the underlying structure of a given situation. In vertical mathematization, a new...

https://link.springer.com/referenceworkentry/10.1007/978-1-4419-1428-6_516

 

[Michael 345]

Both

Personally I go with only INVENTED

While I agree nice patterns were discovered the math to describe was invented

This agrees with your both point of view

https://www-sciencefocus-com.cdn.ampproject.org/v/s/www.sciencefocus.com/science/was-maths-invented-or-discovered/amp/?amp_js_v=a3&amp_gsa=1&usqp=mq331AQFKAGwASA=#aoh=15987355054157&csi=1&referrer=https://www.google.com&amp_tf=From %1$s&ampshare=https://www.sciencefocus.com/science/was-maths-invented-or-discovered/

However I would disagree on the basis mentioned above. We discover nice patterns but nice patterns, in and of themselves, are not math. They BECOME mathematical AFTER we invent math to describe them

Math is a abstract human construct and while the pretty patterns were laying around to be discovered, the pretty patterns are / were the result of physics THEN math was invented to describe

 

[Write4U]

We discover nice patterns but nice patterns, in and of themselves, are not math. They BECOME mathematical AFTER we invent math to describe them

I disagree.
The patterns in and of themselves are of a mathematical nature. It is the regularity of occurrence (a mathematical probability or Implicate) that determines the type of mathematical pattern and the mathematical equations that underlie their self-formation.

Mathematical patterns have existed in nature since the chaotic beginning of the universe. Hence the Chaos Theory! The way reality expresses itself is by way of patterns which are implicated in their relational values and interactive functions.

Man recognized thesepatterns and was able to invent the symbolic language which (hopefully) accurately describes the represented fundamental natural "values" and "functions".

There can be no continued existence without possessing mathematical qualities. The Higgs boson cannot exist in our dimension, but the application of practical dynamic values, we teased it from the Higgs field and could observe it's traces in our dimension when we looked with the Cern collider, before they completely decay into even simpler values which are no longer measurable as physical stuff.

Event display of a candidate Higgs-boson decay to a photon and a Z boson, where the Z boson decays to two muons (shown in red). Green rectangles correspond to energy deposits in cells of the electromagnetic calorimeter, while yellow rectangles correspond to energy deposits in cells of the hadron calorimeter. (Image: ATLAS Collaboration/CERN)

The Higgs boson was discovered by the ATLAS and CMS Collaborations at CERN’s Large Hadron Collider (LHC) in 2012 through its decays into pairs of photons,W bosons and Z bosons. Since then, physicists at these experiments have gained great insight into the properties of the Higgs boson through the study of its different production and decay processes. Decays to pairs of tau leptons and bottom quarks were established, as was the coupling to top quarks. However, the question remains whether the Higgs boson may also interact with yet-unknown particles or forces.

https://atlas.cern/updates/physics-briefing/higgs-photon-z-boson#

While this may appear to be phyical when illustrated, it cannot claim that physical qualities represent a guiding equation, but rather the mathematical values they represent. At Planck scale reality appears to be illogical with all kinds of unpredictable variables, i.e. Chaos !
But according to chaos theory, mathematical values and patterns self-form from chaos, resulting in measurable orders of reality.

It's ALL mathematical, physics included....

Mathematics are the "common denominator" of every extant thing (mathematical pattern), in the universe, whether we have discovered it or not.

All mathematics are discovered by the specific observable patterns physics expresses itself.
We have not yet been able to observe and "symbolize" them all. But we are getting both farther out and deeper into the mystery of the dynamical causal essence of spacetime fabric.

Is it the chaotic language of undefined physics? Irreducible complexity?
Or is the orderly language of observable mathematical patterns? Quasi-intelligent Hierarchy of mathematical Orders?

p.s. IMO. Logic is a form of Quasi-Intelligent chronology. a mathematical Guiding Equation.

And it resolves all conflicting metaphysical interpretations of consciousness and intelligent design. It's Mathematical.......

 

[iceaura]

Just stuff? You cannot see the expressed mathematical orders in these examples ?

The order expressed in those examples was not mathematical, but chemical and physical and evolutionary and so forth.
In several of those examples we - the human theorists and creators of mathematics - have not yet succeeded in inventing the math we need to fully describe the order we observe. We cannot observe such a mathematical order, no matter how detailed and complete our observation, because it isn't there yet: it will be our invention, later on, if we are clever enough.

 

[Write4U]

The order expressed in those examples was not mathematical, but chemical and physical and evolutionary and so forth.
In several of those examples we - the human theorists and creators of mathematics - have not yet succeeded in inventing the math we need to fully describe the order we observe. We cannot observe such a mathematical order, no matter how detailed and complete our observation, because it isn't there yet: it will be our invention, later on, if we are clever enough.

I disagree, if it is observable, it is no longer hidden and will most assuredly answer to one or several of our related sciences. The point is that we cannot yet observe everything, but that our "understanding" of the fundamental rules (constants) of relational mathematical values and functions, allows us to independently arrive at a theoretical mathematical answer before the question is even posed.

Mathematics is the language of the Implicate Order, the single common denominator that holds it all together and provides the dynamic frame of reference for self-expression.

p.s. "common denominator" is a mathematical expression...

 

[Xelasnave.1947]

Mathematics is the language

Does it have cuss words? Can it express love or fear or hope? Can it form the basis of a legal document?
Maybe language is not the right word.

Mathematics is the language of the Implicate Order, the single common denominator that holds it all together and provides the dynamic frame of reference for self-expression.

That is an extrodinary claim can you offer evidence in support? And the reference to self expression do you mean painting by numbers?
Alex

 

[Write4U]

Does it have cuss words? Can it express love or fear or hope? Can it form the basis of a legal document?
Maybe language is not the right word.

In science I believe it's called the "mechanics", not the emotional outbursts of an impressionable person. That's religion.

That is an extrodinary claim can you offer evidence in support?

Yep, the Higgs experiment.

And the reference to self expression do you mean painting by numbers?
Alex

No, I mean the spontaneous self-organization of regular patterns emerging from a prior chaotic disordered state, by way of a guiding equation resting on the relational interactive behaviors of specific inherent values processed in a logical way by an applicable mathematical function.

When all the values of an interaction are present, a mathematical implication of the result is formed before it is actually expressed as a physical phenomenon. The Implicate order, it is a property of a deterministic universe.

An equation is a self-referential expression of a mathematical relationship or comparison. Check out Tupper's Theory.

https://plus.maths.org/content/formula-plots-almost-everything

 

[Seattle]

What is the natural language for what we call a tree in English. If man wasn't here the tree would still be here. What is the natural language for describing a "tree"? It wouldn't be a fractal. A fractal is an approximation.

 

[Neddy Bate]

Yeah...

 

[Write4U]

What is the natural language for what we call a tree in English. If man wasn't here the tree would still be here. What is the natural language for describing a "tree"? It wouldn't be a fractal. A fractal is an approximation.

How would physics describe a tree? A bunch of leaves on branches sprouting from the side of the tree trunk?

All mathematical expressions in nature are approximations of a true mathematical pattern. In a dynamical enviroment all things are in constant change. The key is whether the change is purely random or if change still happens in accordandance with mathematical guiding equations.

In the case of a tree it is the entire object that fractal in nature, i.e. self-similar in its dynamic growth patterns. These are some idealized mathematical common recursive self-referential patterns of a trees.

Recursive Function

A recursive function is an alternative to using iteration. A function is a recursive function if:

It includes a call to itself,
It has a stopping condition to stop the recursion.

https://www.101computing.net/recursive-tree-challenge/

Chapter 8. Fractals
“Pathological monsters! cried the terrified mathematician
Every one of them a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set
The Sierpinski Gasket makes me wanna cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoit Mandelbrot was born”
— Jonathan Coulton, lyrics from “Mandelbrot Set”

Once upon a time, I took a course in high school called “Geometry.” Perhaps you did too. You learned about shapes in one dimension, two dimensions, and maybe even three. What is the circumference of a circle? The area of a rectangle? The distance between a point and a line? Come to think of it, we’ve been studying geometry all along in this book, using vectors to describe the motion of bodies in Cartesian space. This sort of geometry is generally referred to as Euclidean geometry, after the Greek mathematician Euclid.

Figure 8.1

For us nature coders, we have to ask the question: Can we describe our world with Euclidean geometry? The LCD screen I’m staring at right now sure looks like a rectangle. And the plum I ate this morning is circular. But what if I were to look further, and consider the trees that line the street, the leaves that hang off those trees, the lightning from last night’s thunderstorm, the cauliflower I ate for dinner, the blood vessels in my body, and the mountains and coastlines that cover land beyond New York City? Most of the stuff you find in nature cannot be described by the idealized geometrical forms of Euclidean geometry. So if we want to start building computational designs with patterns beyond the simple shapes ellipse(), rect(), and line(), it’s time for us to learn about the concepts behind and techniques for simulating the geometry of nature: fractals.

https://natureofcode.com/book/chapter-8-fractals/

No one expects that the Platonic solids are perfectly expressed as physical objects in nature. It's impossible.
Environmental pressures (external values) always interfere with undisturbed growth.

Mathematical perfection in nature is an abstraction, in reality always an approximation, but that's not the point. It is the growth function that remains a mathematical constant, not the physical environment.

 

[Michael 345]

How would physics describe a tree? A bunch of leaves on branches sprouting from the side of the tree trunk?

Your description is in English not Physics

Physics is a branch of science, not a language

In English it could be described as

A biological system which uses photosynthesis to grow its components

Physics (of both the growth of the future tree and the environment) dictates the growth pathways available and which pathways maximises photosynthesis

I could, but I won't, go into exquisite detail of the resistance of the soil, the maximum speed a tree root could grow in said soil, the strength and breaking point (when the force applied exceeds the resistance of the material the root is composed of) of the root

Giving a physics description of growth is not required to understand a physical item (stuff) follows physics reality laws

 

[Seattle]

How would physics describe a tree? A bunch of leaves on branches sprouting from the side of the tree trunk?

All mathematical expressions in nature are approximations of a true mathematical pattern. In a dynamical enviroment all things are in constant change. The key is whether the change is purely random or if change still happens in accordandance with mathematical guiding equations.

In the case of a tree it is the entire object that fractal in nature, i.e. self-similar in its dynamic growth patterns. These are some idealized mathematical common recursive self-referential patterns of a trees.

Recursive Function

A recursive function is an alternative to using iteration. A function is a recursive function if:

It includes a call to itself,
It has a stopping condition to stop the recursion.

https://www.101computing.net/recursive-tree-challenge/

Chapter 8. Fractals
“Pathological monsters! cried the terrified mathematician
Every one of them a splinter in my eye
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set
The Sierpinski Gasket makes me wanna cry
And a million miles away a butterfly flapped its wings
On a cold November day a man named Benoit Mandelbrot was born”
— Jonathan Coulton, lyrics from “Mandelbrot Set”

Figure 8.1


https://natureofcode.com/book/chapter-8-fractals/

No one expects that the Platonic solids are perfectly expressed as physical objects in nature. It's impossible.
Environmental pressures (external values) always interfere with undisturbed growth.

Mathematical perfection in nature is an abstraction, in reality always an approximation, but that's not the point. It is the growth function that remains a mathematical constant, not the physical environment.

Two identical oak trees will grow differently due to the physical environment.

Physics is the way humans describe a tree. You like to talk about a "natural" language apart from humans.