invariance of scale (split from Evolution not limited to life on earth?)

[Luc Turpin]

On 12/18/2023 at 9:31 AM, Phi for All said:

!

Moderator Note

This isn't a classroom either. It's a discussion forum. What would you like to discuss regarding evolution on other planets? Please design opening posts to encourage an interesting conversation, in this case on a specific aspect of this article.

 

I wish to talk about invariance of scale. The complexity theory version of invariance of scale.  This phenomenon is intriguing, and I believe that this might be an example of it. Am-i right in my assessment? I also would like to know if there are similarities between the physics and complexity sense of invariance of scale? Hope that I am doing it correctly this time!

[exchemist]

21 minutes ago, Luc Turpin said:

I wish to talk about invariance of scale. The complexity theory version of invariance of scale.  This phenomenon is intriguing, and I believe that this might be an example of it. Am-i right in my assessment? I also would like to know if there are similarities between the physics and complexity sense of invariance of scale? Hope that I am doing it correctly this time!

What “phenomenon”  are you talking about, and in what way do you think invariance of scale applies to it?

[Phi for All]

12 minutes ago, exchemist said:

What “phenomenon”  are you talking about, and in what way do you think invariance of scale applies to it?

I'm assuming it's the bit mentioned in the article, the evolutionary process supposedly affecting inorganic systems as well as organic. :

Quote

 

The same sort of evolution happens in the mineral kingdom. The earliest minerals represent particularly stable arrangements of atoms. Those primordial minerals provided foundations for the next generations of minerals, which participated in life's origins. The evolution of life and minerals are intertwined, as life uses minerals for shells, teeth, and bones.

Indeed, Earth's minerals, which began with about 20 at the dawn of our solar system, now number almost 6,000 known today thanks to ever more complex physical, chemical, and ultimately biological processes over 4.5 billion years.

 

[exchemist]

2 minutes ago, Phi for All said:

I'm assuming it's the bit mentioned in the article, the evolutionary process supposedly affecting inorganic systems as well as organic. :

OK. Where would scale come into this? Or is this about “scale” , i.e the degree, of complexity? 

[studiot]

48 minutes ago, exchemist said:

What “phenomenon”  are you talking about, and in what way do you think invariance of scale applies to it?

Excellent question +1

 

I did read the article and I'm sorry but I think find it to be a load of wishful thinking without proper scientific scrutiny.

Befor the quote phi selected we have this peach

 

Quote

The most basic function is stability—stable arrangements of atoms or molecules are selected to continue. Also chosen to persist are dynamic systems with ongoing supplies of energy.

it suffers from the same lack of scrutinity of conservation of mechanical energy as

Quote

The same sort of evolution happens in the mineral kingdom. The earliest minerals represent particularly stable arrangements of atoms. Those primordial minerals provided foundations for the next generations of minerals, which participated in life's origins. The evolution of life and minerals are intertwined, as life uses minerals for shells, teeth, and bones.

 

The temperature of protoearth is estimated at 2300^oK  (NOAA)

Are whatever 'minerals'  that are stable at 2300^oK also stable esp magnetically at 230^oK  ?

 

As a matter of interest I did see a much more plausible 'evolution' of mineral structures into natural radio transmitters as a basis for a scifi story in the mid 1960s.

 

Edited December 19, 2023 by studiot

[Luc Turpin]

7 minutes ago, Phi for All said:

I'm assuming it's the bit mentioned in the article, the evolutionary process supposedly affecting inorganic systems as well as organic. :

Correct! Need to be more specific.

 

2 minutes ago, exchemist said:

OK. Where would scale come into this? Or is this about “scale” , i.e the degree, of complexity? 

Invariance of scale is not mentioned in the article. I am asking if it has anything to do with the fact that we can supposedly find (evolutionary process) in inorganic systems as well as organic.  Not necessarily the degree of complexity, but invariance of scale as one found more broadly from the microscopic to the macroscopic . I am using the complexity definition of invariance of scale as I think that the mathematical-physics version might be different. e.g. Patterning, diversity and complexity supposedly found in inorganic and organic have a relationship (are due to, caused by) the invariance scale concept. Is this statement valid?

 

[studiot]

18 minutes ago, Luc Turpin said:

Patterning, diversity and complexity supposedly found in inorganic and organic have a relationship (are due to, caused by) the invariance scale concept. Is this statement valid?

If it is valid why are the stripes of Equus grevyi different from the stripes of Equus burchelli  ?

[Luc Turpin]

15 minutes ago, studiot said:

If it is valid why are the stripes of Equus grevyi different from the stripes of Equus burchelli  ?

If I understood correctly the article and your post, the stripes of Equus grevyi are not different but the same as the stripes of Equis burchelli!

And I guess that you are telling me that they are different

Similar but still different.

 

[studiot]

1 hour ago, Luc Turpin said:

If I understood correctly the article and your post, the stripes of Equus grevyi are not different but the same as the stripes of Equis burchelli!

And I guess that you are telling me that they are different

Similar but still different.

 

If you want to find out more, get hold of a copy og this book from Oxford university.

It deals with all sorts of organic and inorganic self organisation (pattern forming) including fractal and cellular automata.

There are pages of good references in the back.

 

Here is the excerpt about the zebras.

 

[exchemist]

2 hours ago, Luc Turpin said:

Correct! Need to be more specific.

 

Invariance of scale is not mentioned in the article. I am asking if it has anything to do with the fact that we can supposedly find (evolutionary process) in inorganic systems as well as organic.  Not necessarily the degree of complexity, but invariance of scale as one found more broadly from the microscopic to the macroscopic . I am using the complexity definition of invariance of scale as I think that the mathematical-physics version might be different. e.g. Patterning, diversity and complexity supposedly found in inorganic and organic have a relationship (are due to, caused by) the invariance scale concept. Is this statement valid?

 

Your statement seems to be meaningless. To start with, what is this "complexity definition of invariance of scale"? Where can we find it? Can you recite what it is?

Next, having established that, if we can, you need to explain what you mean by patterning, diversity and complexity being related due to this. 

 

[Luc Turpin]

3 minutes ago, studiot said:

If you want to find out more, get hold of a copy og this book from Oxford university.

It deals with all sorts of organic and inorganic self organisation (pattern forming) including fractal and cellular automata.

There are pages of good references in the back.

 

Here is the excerpt about the zebras.

 

Will do that

1 minute ago, exchemist said:

Your statement seems to be meaningless. To start with, what is this "complexity definition of invariance of scale"? Where can we find it? Can you recite what it is?

Next, having established that, if we can, you need to explain what you mean by patterning, diversity and complexity being related due to this. 

 

In documentation that I read on complexity, there is talk of invariance of scale. For example, shapes are invariant on a small and large scale; as in fractals when you zoom in and out, but still get basically the same shape. 
 

taking the fractal example again, there is a pattern of shape, not all shapes look exactly the same, the complexity-richness of pattern. Find a fractal site on the net to visualize the meanings of these terms

[exchemist]

27 minutes ago, Luc Turpin said:

Will do that

In documentation that I read on complexity, there is talk of invariance of scale. For example, shapes are invariant on a small and large scale; as in fractals when you zoom in and out, but still get basically the same shape. 
 

taking the fractal example again, there is a pattern of shape, not all shapes look exactly the same, the complexity-richness of pattern. Find a fractal site on the net to visualize the meanings of these terms

OK, yes I know that fractals exhibit the same patterns at different scales. But how is that applicable to systems as different as a mineral crystal and a living organism? 

[guidoLamoto]

These guys are a little late to the party. The Universe runs according to probablities and The Minimum Principle. Darwin's theory is really just a specific case as  it relates to biology. Self-organization is a natural consequence of those two rules.  S Kauffman's The Origins of Order is an excellent summary of this, and JD Murray has done a ton of work in many different areas of biology applying it. The zebra pictures above are from his work and summarized in his book Mathematical Biology. If Dr. Falsi had read that, he wouldnt have told us to isolate to deal with CoViD....BTW- the stripe pattern of Zebras is a special application of the Laplacian equation that also applies to epidemics-- the zebra's stripes and the wave pattern of an epidemic are mathematically related. 

[studiot]

1 hour ago, guidoLamoto said:

These guys are a little late to the party.

I don't know whom you are referring to but it could be taken to be insulting.

Nothing to do with me, but I see you are accumulating negative rep points, be warned about the story of the dog.

 

1 hour ago, guidoLamoto said:

The Universe runs according to probablities and The Minimum Principle. Darwin's theory is really just a specific case as  it relates to biology. Self-organization is a natural consequence of those two rules.  S Kauffman's The Origins of Order is an excellent summary of this, and JD Murray has done a ton of work in many different areas of biology applying it. The zebra pictures above are from his work and summarized in his book Mathematical Biology. If Dr. Falsi had read that, he wouldnt have told us to isolate to deal with CoViD....BTW- the stripe pattern of Zebras is a special application of the Laplacian equation that also applies to epidemics-- the zebra's stripes and the wave pattern of an epidemic are mathematically related. 

There is actually quite a bit of truth in the rest of your post, pity there were so amny points each too short and without support.

Nevertheless

Yes Murray did the work on the Zebras, as was acknowledged in my reference.

I assume by Dr Falsi you mean Dr Fauci  ?

I also assume you think isolation was wrong ?

I would be interested to see you apply the very simple Laplace equation to obtain the kind of chemical and biochemical phenomena we are talking about.
What function are you connecting in space and time ?

You are correct in that there is a substantial probability element in epidemic modelling. This link was proven and started more than a century before Covid By Ross.

[Luc Turpin]

5 hours ago, exchemist said:

OK, yes I know that fractals exhibit the same patterns at different scales. But how is that applicable to systems as different as a mineral crystal and a living organism? 

I could have asked a better question: second attemps - What is the factor that makes evolution appear in non-living as well as in living form? What is the common denominator? Does invariance of scale have anything to do with it?

As for the quote above, are you asking how fractals are applicable to systems as different as a mineral crystal and a living organism? Respectfully, its the fractal shape found in living things (human brains https://fractalfoundation.org/OFC/OFC-1-6.html#:~:text=Our brains are full of,connections%2C among these brain cells.) and non-living (coastline: https://fractalfoundation.org/OFC/OFC-10-4.html). As for mineral crystal, they seem also to be fractal in nature.

[swansont]

26 minutes ago, Luc Turpin said:

I could have asked a better question: second attemps - What is the factor that makes evolution appear in non-living as well as in living form? What is the common denominator? Does invariance of scale have anything to do with it?

Evolution is a feedback loop. So, too, would be a system that can be rearranged and where selection takes place.

[Luc Turpin]

28 minutes ago, swansont said:

Evolution is a feedback loop. So, too, would be a system that can be rearranged and where selection takes place.

Understood

[exchemist]

9 hours ago, Luc Turpin said:

I could have asked a better question: second attemps - What is the factor that makes evolution appear in non-living as well as in living form? What is the common denominator? Does invariance of scale have anything to do with it?

As for the quote above, are you asking how fractals are applicable to systems as different as a mineral crystal and a living organism? Respectfully, its the fractal shape found in living things (human brains https://fractalfoundation.org/OFC/OFC-1-6.html#:~:text=Our brains are full of,connections%2C among these brain cells.) and non-living (coastline: https://fractalfoundation.org/OFC/OFC-10-4.html). As for mineral crystal, they seem also to be fractal in nature.

Why do you think mineral crystals are fractal in nature?

[Luc Turpin]

9 hours ago, swansont said:

Evolution is a feedback loop. So, too, would be a system that can be rearranged and where selection takes place.

Let me see if I get it right: the microscopic and macroscopic are similar because both are of the physical and share features such as patterning, diversity, complexity, etc., and this similarity of features present at difference size scale is called invariance of scale. For evolution, its a feedback loop feature that makes it similar for natural evolution versus evolution of planets, stars, atoms, etc. Patterning, diversity, complexity and to that effect, invariance of scale does not apply because natural evolution is a theory-idea-concept, and not a thing! Right?

1 hour ago, exchemist said:

Why do you think mineral crystals are fractal in nature?

This is not an area of interest for me, so I know very little.  Searched the net and got these references https://www.sciencedirect.com/science/article/abs/pii/001282529090027S and https://www.degruyter.com/document/doi/10.2138/am-2021-7698/pdf

I think, maybe wrongly, that they somehow link mineral crystals to fractals.

 

[studiot]

33 minutes ago, Luc Turpin said:

Let me see if I get it right: the microscopic and macroscopic are similar because both are of the physical and share features such as patterning, diversity, complexity, etc., and this similarity of features present at difference size scale is called invariance of scale. For evolution, its a feedback loop feature that makes it similar for natural evolution versus evolution of planets, stars, atoms, etc. Patterning, diversity, complexity and to that effect, invariance of scale does not apply because natural evolution is a theory-idea-concept, and not a thing! Right?

 

10 hours ago, swansont said:

Evolution is a feedback loop. So, too, would be a system that can be rearranged and where selection takes place.

 

16 hours ago, guidoLamoto said:

BTW- the stripe pattern of Zebras is a special application of the Laplacian equation

 

Although Ball does not go into the rather complicated mathematics of chemical kinetics he does outline the Activator - Inhibitor nature of the origin of zebra stripes.

This outline shows clearly that the biochemical reactions are what a pair of intertwined multistep reactions.

Each has its own differential equation and the set of equations are linked by something akin to a feedback system.

Such systems can be pretty complicated and we are only just at the beginning of being able to solve them.

 

1 hour ago, exchemist said:

Why do you think mineral crystals are fractal in nature?

Exchemist is quite right to push this.

42 minutes ago, Luc Turpin said:

This is not an area of interest for me, so I know very little.  Searched the net and got these references https://www.sciencedirect.com/science/article/abs/pii/001282529090027S and https://www.degruyter.com/document/doi/10.2138/am-2021-7698/pdf

I think, maybe wrongly, that they somehow link mineral crystals to fractals.

When I have time I will read your article.

Meanwhile you need to make a clear distinction between individual crystals and crystal systems and their growth.  They are not the same or subject to the same laws.

Perfect individual crystals always have regular non fractal geometry.

But there are several different effects that apply to the growth of crystal systems.

I wonder if the articles are thinking of snowflakes  or other dendritic structures ?

 

Dendrites occur when a crystal can basically  grow freely. That is it is not restricted in the space around it.

They occur because of self interaction between growing parts of of the structure and result in the structural branching so characteristic of snowflakes.

But the flakes are made of lots of individual perfect small crystals and do not exhibit this branching at the scale of individual cystals or smaller.

 

The 'Koch Snowflake' models this, but as a mathematical construct it is truly scale independent and therefore fractal.

 

Geologists are well used to ordering the sequence of solidifying minerals from a magma melt because the solidifying minerals are often intruded into cracks and other confined spaces so the mineral that solidifies first out of the magma will have all the space available and form the most nearly perfect crystals. The next mineral to solidify would have to fill the gaps and so on, resulting in malformed crystals, truncated at rock boundaries.

It can also be a way of distinguishing whether volcanic rocks are intrusive or extrusive.

In this case there is no fractal aspect to the process at all.

 

[Luc Turpin]

30 minutes ago, studiot said:

 

 

 

Although Ball does not go into the rather complicated mathematics of chemical kinetics he does outline the Activator - Inhibitor nature of the origin of zebra stripes.

This outline shows clearly that the biochemical reactions are what a pair of intertwined multistep reactions.

Each has its own differential equation and the set of equations are linked by something akin to a feedback system.

Such systems can be pretty complicated and we are only just at the beginning of being able to solve them.

 

Exchemist is quite right to push this.

When I have time I will read your article.

Meanwhile you need to make a clear distinction between individual crystals and crystal systems and their growth.  They are not the same or subject to the same laws.

Perfect individual crystals always have regular non fractal geometry.

But there are several different effects that apply to the growth of crystal systems.

I wonder if the articles are thinking of snowflakes  or other dendritic structures ?

 

Dendrites occur when a crystal can basically  grow freely. That is it is not restricted in the space around it.

They occur because of self interaction between growing parts of of the structure and result in the structural branching so characteristic of snowflakes.

But the flakes are made of lots of individual perfect small crystals and do not exhibit this branching at the scale of individual cystals or smaller.

 

The 'Koch Snowflake' models this, but as a mathematical construct it is truly scale independent and therefore fractal.

 

Geologists are well used to ordering the sequence of solidifying minerals from a magma melt because the solidifying minerals are often intruded into cracks and other confined spaces so the mineral that solidifies first out of the magma will have all the space available and form the most nearly perfect crystals. The next mineral to solidify would have to fill the gaps and so on, resulting in malformed crystals, truncated at rock boundaries.

It can also be a way of distinguishing whether volcanic rocks are intrusive or extrusive.

In this case there is no fractal aspect to the process at all.

 

As stated, I have very limited knowledge of crystals, so I will let you and exchemist lead the way on this one

[swansont]

2 hours ago, Luc Turpin said:

Let me see if I get it right: the microscopic and macroscopic are similar because both are of the physical and share features such as patterning, diversity, complexity, etc., and this similarity of features present at difference size scale is called invariance of scale. For evolution, its a feedback loop feature that makes it similar for natural evolution versus evolution of planets, stars, atoms, etc. Patterning, diversity, complexity and to that effect, invariance of scale does not apply because natural evolution is a theory-idea-concept, and not a thing! Right?

Complexity, diversity and patterning can happen at almost any scale, but that does not mean it is invariant. Larger structures could possibly be more complex just because there are more parts that can be rearranged. Or less complex because certain configurations are unstable or otherwise not functional. For some structures, the fact that surfaces scale differently than volume will be important; it will mean that small structures necessarily look different than large ones. 

If there’s some overall rule about this, one can go look for it, but it’s not going to be adequately described, to the point we can discuss it, in a popular summary of the science, like the physorg article. Primary sources are better.

 

[joigus]

Keywords to look up:

Scale invariance and critical phenomena

Universality

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

It seems to be the case that when changes in structure formation are about to happen, a transitory stage characterised by scale invariance happens. An example is a gas about to make the transition to a liquid.

But, as noted, you could have some cases of self-similarity (synonym of scale invariance) when or where no phase transition is involved. Examples: biological tissue patterns, the shape of the coastline, etc.

Another kind of self-similarity seems to be in evolution itself, but not like a spatial pattern. Rather, as a pattern of embedded behaviour: A thing trying to pass on as good as possible a copy of its identity, with little things inside trying to pass on as good as possible copies of their identity,... up to a final level (chuncks of nucleic acid) of little things trying to pass on as good as possible a partial copy of their identity.

And so on, which seem to be relevant words here.

[Luc Turpin]

2 hours ago, joigus said:

Keywords to look up:

Scale invariance and critical phenomena

Universality

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

It seems to be the case that when changes in structure formation are about to happen, a transitory stage characterised by scale invariance happens. An example is a gas about to make the transition to a liquid.

But, as noted, you could have some cases of self-similarity (synonym of scale invariance) when or where no phase transition is involved. Examples: biological tissue patterns, the shape of the coastline, etc.

Another kind of self-similarity seems to be in evolution itself, but not like a spatial pattern. Rather, as a pattern of embedded behaviour: A thing trying to pass on as good as possible a copy of its identity, with little things inside trying to pass on as good as possible copies of their identity,... up to a final level (chuncks of nucleic acid) of little things trying to pass on as good as possible a partial copy of their identity.

And so on, which seem to be relevant words here.

So, self-similarity being synonym of scale invariance, both together forming a universal process in nature! correct?

Spatial pattern in objects and embedded behaviour in natural evolution! correct?

What about living organisms? spatial pattern, embedded behaviour or both?

[joigus]

2 hours ago, Luc Turpin said:

So, self-similarity being synonym of scale invariance, both together forming a universal process in nature! correct?

It's a mathematical pattern rather than a process. I'm sure something like that is the reason behind @exchemist's excellent question.

Take. eg, principles of extremal time, action, length, etc. They appear everywhere in physics. It's more about a recurring mathematical theme than actually a particular process.