Why are things in space the shape that they are?

[Write4U]

View attachment 3589

I much prefer

View attachment 3590

Cheers

You could not have the latter without the first.

p.s. notice the "Golden Ratio" in that beautiful spiral galaxy? The Fibonacci sequence in grand display.

 

[DaveC426913]

p.s. notice the "Golden Ratio" in that beautiful spiral galaxy? The Fibonacci sequence in grand display.

Nope.
Galaxy arms do not follow the Golden Ratio.

Just because two things have a superficial similarity does not mean they are shaped by the same forces.

You have been duped by Pop Sci.

 

[Write4U]

I have presented Roger Antonsen before, but this bears reintroduction for illustrative purposes
Good stuff.
If anything do watch a few moments starting @ 8:30 to watch the self-ordering image of a dynamic 4/3 ratio.

 

[Write4U]

Nope.
Galaxy arms do not follow the Golden Ratio.
Just because two things have a superficial similarity does not mean they are shaped by the same forces.
You have been duped by Pop Sci.

There is no perfect mathematical pattern in nature. It is practically impossible. Nature is a dynamical environment.
There is no requirement of mathematical exactness. There are only guiding equations.

Patterns in nature


Natural patterns form as wind blows sand in the dunes of the Namib Desert. The crescent shaped dunes and the ripples on their surfaces repeat wherever there are suitable conditions.


Patterns of the veiled chameleon, Chamaeleo calyptratus, provide camouflage and signal mood as well as breeding condition.

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

https://www.google.com/search?q=golden%20ratio%20in%20nature&tbm=isch&tbs=rimg%3ACejTOTkfHtoTYRsCFQsZzBWc&hl=en&sa=X&ved=0CBsQuIIBahcKEwjgvprPyZvrAhUAAAAAHQAAAAAQCQ&biw=1264&bih=615

 

[paddoboy]

p.s. notice the "Golden Ratio" in that beautiful spiral galaxy? The Fibonacci sequence in grand display.

There are many different types of spirals with regards to galaxies in the universe, including the barred spiral of which the Milky Way is one.These are classified as SB. Other photos of spiral galaxies also exhibit a vast array of different types. All those spiral galaxies have a few things in common...they are a result of gravity first and foremost, secondly angular momentum and density waves.
In essence the spiral arms of galaxies are not permanent structures, and stars continually move in and out of these areas over time. Another important point to remember,
"There were no spiral galaxies in the early universe" they were just conglomerations of stars formed in spherical clumps.

https://www.universetoday.com/110929/why-do-galaxies-have-arms/#:~:text=Each one with twisting arms,them this characteristic spiral shape


Not quite into this "Fibonacci" sequence or golden ration stuff, but would this be another accidental example?
https://www.quora.com/Do-spiral-galaxies-follow-the-golden-ratio

 

[Write4U]

Clever?
IMO, you seems to be missing the grand artistry emerging from natural selection of efficient self-organizing (mathematical) patterns in Nature.
---------------------------------------------------------------------------------------------------------
I am giving you examples of one guiding equation of self-organizing shapes in nature. It is part of the natural selection favoring self-similar fractality over random growth in nature. Self-similarity is an "efficient" growth pattern.

Think about it!

Golden spiral

Golden spirals are self-similar. The shape is infinitely repeated when magnified.
In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio.[1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.

Spirals in nature

Approximate logarithmic spirals can occur in nature, for example the arms of spiral galaxies[3] - golden spirals are one special case of these logarithmic spirals, although there is no evidence that there is any general tendency towards this case appearing. Phyllotaxis is connected with the golden ratio because it involves successive leaves or petals being separated by the golden angle; it also results in the emergence of spirals, although again none of them are (necessarily) golden spirals. It is sometimes stated that spiral galaxies and nautilus shells get wider in the pattern of a golden spiral, and hence are related to both φ and the Fibonacci series.[4] In truth, spiral galaxies and nautilus shells (and many mollusk shells) exhibit logarithmic spiral growth, but at a variety of angles usually distinctly different from that of the golden spiral.[5][6][7] This pattern allows the organism to grow without changing shape.

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

Research and Reflection: Fractals, the Fibonacci Spiral, and Nature

“A fractal is a way of seeing infinity.” – Benoit Mandelbrot

Fibonacci numbers were officially discovered by Leonardo of Pisa, but have existed in the universe for as long as we know. These numbers appear in nanoparticles13, black holes13, spiral galaxies16, flowers17, human anatomy13, and DNA nucleotides18

The Fibonacci spiral, however, is a particularly fascinating application because of its mathematical perfection, aesthetic appeal, and biological importance.

One notable example of natural Fibonacci spiraling, is the arrangement of leaves, seeds, and petals in plants. For instance, the seeds in the center of a sunflower follow a perfect Fibonacci spiraling pattern, which allows for an efficient usage of space, and maximal seed packing. Looking at the leaf arrangement around the stem in many herbaceous plants (a study known as phyllotaxis13) reveals that the leaves are arranged in an identical spiraling pattern.

In this case, the Fibonacci spiral benefits the plant by maximizing exposure of leaves to sunlight, and by aiding in even distribution of water17. From biological and evolutionary perspectives, the phi ratio and the Fibonacci spiral are essential to the structure, function, and survival of many organisms.

The Fibonacci spiral in Romanesco Broccoli http://from-bedroom-to-study.blogspot.com/2012/09/the-swirly-spirals-of-natures-numbers.html

The Fibonacci spiral arrangement of leaves around a plant stem http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

https://blogs.uoregon.edu/mjanesaad...ch-fractals-the-fibonacci-spiral-and-nature/#

 

[Xelasnave.1947]

. Self-similarity is an "efficient" growth pattern

Nature invented these patterns or rather they arise from efficiency...the interaction of bubbles for example..I suggest that it "just happens" a predictable response to gravity...order being arrived at without math although math can describe what we observe...and perhaps you place too much importance on the observation believing the language you use to describe your observation had any part to play in how the objects arranged themselves...surely it is only when we stand a human there to observe do we get the maths.

And I find nothing unusual in patterns but I don't think nature goes around with a calculator in its hand.

Consider the bubbles..what is at play..a math formula or just bubbles trying to fit?

Anyways all very interesting I just feel we ( by that I mean you) are missing something really...it's like what came first the chicken or the egg, we we stumped by that one but we now know that the egg came first...and so what came first the maths or just a need to "fit" I think the need to fit comes first the language of humans well after.

Alex

 

[DaveC426913]

Point made more eloquently than I ever could.

 

[DaveC426913]

Approximate logarithmic spirals can occur in nature, for example the arms of spiral galaxies ...

... golden spirals are one special case of these logarithmic spirals, although there is no evidence that there is any general tendency towards this case appearing.

 

[Write4U]

And I find nothing unusual in patterns but I don't think nature goes around with a calculator in its hand.

You may want to rephrase that. Natural Selection is a form of probabilistic mathematical culling the weak and sick. If you fail the test of Natural Selection you will not live to procreate.

Anyways all very interesting I just feel we ( by that I mean you) are missing something really...it's like what came first the chicken or the egg, we e stumped by that one but we now know that the egg came first...and so what came first the maths or just a need to "fit" I think the need to fit comes first the language of humans well after.

What came first is a mathematical equation and shows the chronological evolution of purely round eggs into oval shaped eggs as organisms grew larger?

Natural selection is a "mathematical function", no?

 

[Write4U]

Write4U said: ↑
Approximate logarithmic spirals can occur in nature, for example the arms of spiral galaxies ...

... golden spirals are one special case of these logarithmic spirals, although there is no evidence that there is any general tendency towards this case appearing.

That's right, not all galaxies are "spiral galaxies". The ones that are do follow the Fibonacci "guiding equation".

And to clear up any misunderstanding, Spirals are very much present in nature, especially in plant biology which need to grow vertically toward the sun without falling over and have a maximum surface area for collecting solar energy for photosynthesis.

Spirals in nature
BY ROBERT HARDING · PUBLISHED JANUARY 27, 2014 · UPDATED APRIL 2, 2015

Spirals are patterns that occur naturally in plants and natural systems, including the weather. They were studied by mathematicians including Leonardo Fibonacci, who tried to understand order in nature. Spirals have also been the inspiration for architectural forms and ancient symbols.

Plants like this Aloe follow Fibonacci’s description of Phyllotaxis, a formula for the spiral growth patterns of leaves (age fotostock/Robert Harding)


A colony of salps that has formed itself into a spiral and is floating at the surface of the ocean, off the Channel Islands of California (age fotostock/Robert Harding)
Purely accidental?

https://www.robertharding.com/blog/2014/01/27/spirals-in-nature/#[/quote]

 

[Michael 345]

Purely accidental?

AGAIN - P H Y S I C S

 

[Write4U]

AGAIN - P H Y S I C S

Yep, Physics doing physics in accordance with mathematical "guiding equations"

 

[Michael 345]

Yep, Physics doing physics in accordance with mathematical "guiding equations"

Remember Earthly Physics had been doing Earthly Physics long before Earthly Earthlings came into being and long before Earthly Earthlings invented mathematical guiding equations

So mathematical guiding equations are totally mis named

Better correctly named mathematical DESCRIPTIVE equations

 

[James R]

Er, would that be because the composite figure is in fact not a triangle? There is a kink in the "pseudo-hypotenuse", where the blue and red triangles touch, isn't there?

Spoiler

Yes, you're right. There's a quite extensive wikipedia page on this particular puzzle, which is interesting.

DaveC is right. My point is that attempting to prove things using diagrams is fraught with danger, unless you're careful.

 

[James R]

I saw a fractal in that illustration. (post #72)

There's no fractal there.

In your illustration I saw a incorrect mathematical arrangement of the triangles, which created the mismatch.

What? There's a "correct" way to arrange triangles? That's news to me.

 

[Xelasnave.1947]

You may want to rephrase that.

No I am happy with what I said.

Natural Selection is a form of probabilistic mathematical culling the weak and sick.

Interesting but I did not raise anything along those lines...mathematical culling? Hmmmm I hope predictors know when the percentage allocated to them has been reached.

What came first is a mathematical equation and shows the chronological evolution of purely round eggs into oval shaped eggs as organisms grew larger?

Your question presents as an unsupported claim. Maths is humans language do you suggest that somehow the universe started with pages of equations? Where did the paper come from?

Natural selection is a "mathematical function", no?

Perhaps you could define natural selection as you understand it ..the meaning I attract does not work when I match it with what you say.

Tell me this...rather present a view...on this observation.
If humans did not exist neither would maths.

Alex

 

[Xelasnave.1947]

And why are eggs pointy at one end?...and please no maths in the answer.
Alex

 

[DaveC426913]

A lot of confusion of map versus territory happening here.
Physics is the territory.
Math is the map.

 

[Write4U]

No I am happy with what I said.

Interesting but I did not raise anything along those lines...mathematical culling? Hmmmm I hope predictors know when the percentage allocated to them has been reached.

Natural selection is mathematical process.

How does evolution by natural selection work? Evolution by natural selection is an inevitable, mathematical process. The frequency of a particular allele will change; its rate of change will depend mathematically on the advantage (or relative fitness) of that allele.

MATHS! EEK! This doesn't sound very pleasant, and indeed the maths can get very complicated (though not in 2007). However, much of the excitement in modern evolutionary theory is about theory. Even though we don't expect you to get to grips with all of it, we will try to give you an outline

Mathematical evolutionary theory is useful. For example, given information about natural selection, how rapidly will evolution occur? The answers help us to take precautions about antibiotic resistance, or pest resistance, for instance. Evolution is a predictive science!....more

https://www.ucl.ac.uk/~ucbhdjm/courses/b242/OneGene/OneGene.html#

Your question presents as an unsupported claim. Maths is humans language do you suggest that somehow the universe started with pages of equations? Where did the paper come from?

Physics are a human language also . Does writing "tree" on a piece of paper make tree? Try to do some compartmentalizing.
You need to forget about human mathematics which are only "symbolic" representations of natural
processes and interactions of "relational values" and "mathematical functions".

Perhaps you could define natural selection as you understand it ..the meaning I attract does not work when I match it with what you say.
Tell me this...rather present a view...on this observation.
If humans did not exist neither would maths.
Alex

If human did not exist there would be no human maths. However the universe would function in exactly the same mathematical way as it does now.
It did long before man came on the scene, so if you can ascribe at least some mathematical values and functions to spacetime today, they must have been there all the time, no?

That's what astronomers say.....?