Date: 28/08/2021 01:36:29
From: Tau.Neutrino
ID: 1783425
Subject: Entropy Question

Does Entropy cause complexity? If this is true then, how does order come from disorder?

Reply Quote

Date: 28/08/2021 02:19:40
From: transition
ID: 1783426
Subject: re: Entropy Question

Tau.Neutrino said:


Does Entropy cause complexity? If this is true then, how does order come from disorder?

negentropy ?

say you bank energy up in a system, like earth and its atmosphere, positioned as it is not too far away or too near the sun, here we are on this rotating orbiting rock, patterns gradually emerge, largely courtesy day and night (solar energy cycles), seasonal changes (orbit around the sun, obliquity of ecliptic etc), moon (and sun) causes tides etc, all of which could be seen to clock order into the system, are an ordering force generating a system, and more complex systems potentially, as seems to have happened here locally on earth

day/night cycles clock order for example, have a potential that way, embed order with thermal gradients etc

soon as you have rotating things you have a clock

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Date: 28/08/2021 03:00:06
From: transition
ID: 1783427
Subject: re: Entropy Question

transition said:


Tau.Neutrino said:

Does Entropy cause complexity? If this is true then, how does order come from disorder?

negentropy ?

say you bank energy up in a system, like earth and its atmosphere, positioned as it is not too far away or too near the sun, here we are on this rotating orbiting rock, patterns gradually emerge, largely courtesy day and night (solar energy cycles), seasonal changes (orbit around the sun, obliquity of ecliptic etc), moon (and sun) causes tides etc, all of which could be seen to clock order into the system, are an ordering force generating a system, and more complex systems potentially, as seems to have happened here locally on earth

day/night cycles clock order for example, have a potential that way, embed order with thermal gradients etc

soon as you have rotating things you have a clock

in that above you might see three clocks

consider for a moment just day/night cycles, the rotation of the earth, a reliable rotation, so you’ve got that, it’s a massive influence

now you might want a massive random events generator, within the clocked energy system, and you’d have something potentially very transformative, given enough time

the random events generator could be the hydrological cycle for example, among other possibilities, but water’s good, you’ve got phase transitions, both large bodies and distributed massed of water (seas and clouds for example), and the air you breathe (keeping it simple, there’s much more, large masses of ice for example)

anyway back to the massive random events generator, picture the seas, and the rains on land that wash the soil or whatever, consider mineral wash from the land, sedimentation, stratification

it all makes for a massive random events generator

you’ve got thermal cycles, thermal gradients, that form patterns, all lending to potential structure, transforming structure

if you add a massive random events generator within that, you have the possibility of (further) structure happening, enough accidents, that could result in self-replicating structures

so as things went earth has been and is an exotic free-running chemistry lab, that’s persisted for a long time, long enough to appear exotic to something interested in life exotica anyway, the evolved humans for example

Reply Quote

Date: 28/08/2021 08:05:31
From: Bogsnorkler
ID: 1783437
Subject: re: Entropy Question

Tau.Neutrino said:


Does Entropy cause complexity? If this is true then, how does order come from disorder?

by inputting energy.

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Date: 28/08/2021 09:13:00
From: The Rev Dodgson
ID: 1783444
Subject: re: Entropy Question

Tau.Neutrino said:


Does Entropy cause complexity? If this is true then, how does order come from disorder?

What do you mean by “cause” and “complexity”?

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Date: 28/08/2021 09:17:31
From: The Rev Dodgson
ID: 1783446
Subject: re: Entropy Question

The Rev Dodgson said:


Tau.Neutrino said:

Does Entropy cause complexity? If this is true then, how does order come from disorder?

What do you mean by “cause” and “complexity”?

And while we’re at it, the Internet says that “entropy” means:

a thermodynamic quantity representing the unavailability of a system’s thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.

so I’ll assume that’s what you mean by it as well, unless you say otherwise.

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Date: 28/08/2021 09:21:20
From: The Rev Dodgson
ID: 1783447
Subject: re: Entropy Question

The Rev Dodgson said:


The Rev Dodgson said:

Tau.Neutrino said:

Does Entropy cause complexity? If this is true then, how does order come from disorder?

What do you mean by “cause” and “complexity”?

And while we’re at it, the Internet says that “entropy” means:

a thermodynamic quantity representing the unavailability of a system’s thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.

so I’ll assume that’s what you mean by it as well, unless you say otherwise.

And what about “does”?

Is “is it true that?” a reasonable approximation to your understanding of that word?

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Date: 28/08/2021 10:42:47
From: SCIENCE
ID: 1783473
Subject: re: Entropy Question

surely the information theoretic concept is more fundamental than and has priority over the thermodynamic concept

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Date: 28/08/2021 10:53:35
From: The Rev Dodgson
ID: 1783484
Subject: re: Entropy Question

SCIENCE said:


surely the information theoretic concept is more fundamental than and has priority over the thermodynamic concept

So what is the answer to the question according to the information theoretic concept?

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Date: 28/08/2021 11:03:48
From: Bubblecar
ID: 1783498
Subject: re: Entropy Question

Winding down from a simple, hot, low entropy system to a high entropy system can entail the emergence of much complexity along the way, by shifting energy from fairly simple regions to regions capable of using it for more complex work.

Much of the complexity in our universe was caused by gravity forming stars, which are compact reservoirs of energy that can heat planets (also formed by gravity) moderately and reliably over long periods of time, supporting the emergence of life, cities and internets etc.

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Date: 28/08/2021 11:04:19
From: SCIENCE
ID: 1783500
Subject: re: Entropy Question

The Rev Dodgson said:

SCIENCE said:

surely the information theoretic concept is more fundamental than and has priority over the thermodynamic concept

So what is the answer to the question according to the information theoretic concept?

  1. no
  2. at random
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Date: 28/08/2021 11:13:38
From: The Rev Dodgson
ID: 1783510
Subject: re: Entropy Question

SCIENCE said:


The Rev Dodgson said:

SCIENCE said:

surely the information theoretic concept is more fundamental than and has priority over the thermodynamic concept

So what is the answer to the question according to the information theoretic concept?

  1. no
  2. at random

1. But we don’t yet know what he meant by “complexity”
2. I don’t think that really answers the question
3. What’s with those numbers turning themselves into hash symbols, and vice versa?

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Date: 28/08/2021 11:54:46
From: SCIENCE
ID: 1783521
Subject: re: Entropy Question

The Rev Dodgson said:


SCIENCE said:

The Rev Dodgson said:

So what is the answer to the question according to the information theoretic concept?

  1. no
  2. at random

1. But we don’t yet know what he meant by “complexity”
2. I don’t think that really answers the question
3. What’s with those numbers turning themselves into hash symbols, and vice versa?

  1. surely ‘e would stay in scope and hence consider complexity to be the length of a shortest computer program (in a predetermined programming language) that produces the object as output
  2. sure it does, “how does order come from disorder”, statistically at random
  3. we learnt it from the “Textile mark-up quick reference” below the reply box
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Date: 28/08/2021 12:07:42
From: Bubblecar
ID: 1783526
Subject: re: Entropy Question

Bubblecar said:


Winding down from a simple, hot, low entropy system to a high entropy system can entail the emergence of much complexity along the way, by shifting energy from fairly simple regions to regions capable of using it for more complex work.

Much of the complexity in our universe was caused by gravity forming stars, which are compact reservoirs of energy that can heat planets (also formed by gravity) moderately and reliably over long periods of time, supporting the emergence of life, cities and internets etc.

Stars also of course synthesise new elements from simpler ones by nuclear fusion, thus adding a greater variety of material to the mix of what’s available for other processes to work with, again involving the emergence of more complex structure as the universe winds down.

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Date: 28/08/2021 12:51:16
From: The Rev Dodgson
ID: 1783545
Subject: re: Entropy Question

SCIENCE said:


The Rev Dodgson said:

SCIENCE said:

  1. no
  2. at random

1. But we don’t yet know what he meant by “complexity”
2. I don’t think that really answers the question
3. What’s with those numbers turning themselves into hash symbols, and vice versa?

  1. surely ‘e would stay in scope and hence consider complexity to be the length of a shortest computer program (in a predetermined programming language) that produces the object as output
  2. sure it does, “how does order come from disorder”, statistically at random
  3. we learnt it from the “Textile mark-up quick reference” below the reply box
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Date: 28/08/2021 12:56:36
From: transition
ID: 1783548
Subject: re: Entropy Question

The Rev Dodgson said:


Tau.Neutrino said:

Does Entropy cause complexity? If this is true then, how does order come from disorder?

What do you mean by “cause” and “complexity”?

cause means new mechanisms, that evolve in a developing system, an accident or many accidents that result in something that repeats, even replicates

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Date: 28/08/2021 13:31:20
From: The Rev Dodgson
ID: 1783558
Subject: re: Entropy Question

transition said:


The Rev Dodgson said:

Tau.Neutrino said:

Does Entropy cause complexity? If this is true then, how does order come from disorder?

What do you mean by “cause” and “complexity”?

cause means new mechanisms, that evolve in a developing system, an accident or many accidents that result in something that repeats, even replicates

Thanks.

We’ll see if TN was using the same definition.

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Date: 28/08/2021 13:49:28
From: transition
ID: 1783568
Subject: re: Entropy Question

The Rev Dodgson said:


transition said:

The Rev Dodgson said:

What do you mean by “cause” and “complexity”?

cause means new mechanisms, that evolve in a developing system, an accident or many accidents that result in something that repeats, even replicates

Thanks.

We’ll see if TN was using the same definition.

I was alluding to the stuff out there, independent of concepts, or exists independent of concepts, or emerged independent of concepts, or independent of human conceptualization

stuff that dared happen without a definition

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Date: 28/08/2021 13:58:23
From: The Rev Dodgson
ID: 1783571
Subject: re: Entropy Question

transition said:


The Rev Dodgson said:

transition said:

cause means new mechanisms, that evolve in a developing system, an accident or many accidents that result in something that repeats, even replicates

Thanks.

We’ll see if TN was using the same definition.

I was alluding to the stuff out there, independent of concepts, or exists independent of concepts, or emerged independent of concepts, or independent of human conceptualization

stuff that dared happen without a definition

OK, I’d still like to know what TN meant by the words though.

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Date: 28/08/2021 14:01:55
From: transition
ID: 1783573
Subject: re: Entropy Question

The Rev Dodgson said:


transition said:

The Rev Dodgson said:

Thanks.

We’ll see if TN was using the same definition.

I was alluding to the stuff out there, independent of concepts, or exists independent of concepts, or emerged independent of concepts, or independent of human conceptualization

stuff that dared happen without a definition

OK, I’d still like to know what TN meant by the words though.

as you were, good luck with the enterprise of convergent reality

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Date: 28/08/2021 14:11:30
From: The Rev Dodgson
ID: 1783575
Subject: re: Entropy Question

transition said:


The Rev Dodgson said:

transition said:

I was alluding to the stuff out there, independent of concepts, or exists independent of concepts, or emerged independent of concepts, or independent of human conceptualization

stuff that dared happen without a definition

OK, I’d still like to know what TN meant by the words though.

as you were, good luck with the enterprise of convergent reality

What do you mean by “convergent reality”?

I think I’m OK with the first 7 and the 9th words.

Might come back to “enterprise” later.

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Date: 28/08/2021 14:24:44
From: SCIENCE
ID: 1783584
Subject: re: Entropy Question

The Rev Dodgson said:


SCIENCE said:

The Rev Dodgson said:

1. But we don’t yet know what he meant by “complexity”
2. I don’t think that really answers the question
3. What’s with those numbers turning themselves into hash symbols, and vice versa?

  1. surely ‘e would stay in scope and hence consider complexity to be the length of a shortest computer program (in a predetermined programming language) that produces the object as output
  2. sure it does, “how does order come from disorder”, statistically at random
  3. we learnt it from the “Textile mark-up quick reference” below the reply box
  • I rather doubt that. I’m not even convinced that it’s the right and proper SCIENTIFIC way to approach this question.
  • It may be a random process, but that’s not all it is. There need to be other factors involved.
  • Thanks. I suppose I should read that stuff as well.

(a) sure it is, from before ‘saac to beyond ‘bert great giants of scientists have relied on mathematics to transform their physics
(b) ¿ref, is there some kind of intelligent design perhaps

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Date: 28/08/2021 14:36:51
From: The Rev Dodgson
ID: 1783590
Subject: re: Entropy Question

SCIENCE said:


The Rev Dodgson said:

SCIENCE said:

  1. surely ‘e would stay in scope and hence consider complexity to be the length of a shortest computer program (in a predetermined programming language) that produces the object as output
  2. sure it does, “how does order come from disorder”, statistically at random
  3. we learnt it from the “Textile mark-up quick reference” below the reply box
  • I rather doubt that. I’m not even convinced that it’s the right and proper SCIENTIFIC way to approach this question.
  • It may be a random process, but that’s not all it is. There need to be other factors involved.
  • Thanks. I suppose I should read that stuff as well.

(a) sure it is, from before ‘saac to beyond ‘bert great giants of scientists have relied on mathematics to transform their physics
(b) ¿ref, is there some kind of intelligent design perhaps

(a) Yes they use maths, but that’s not all they use.
(b) No implication of intelligent design. Just different types of processes.

Reply Quote

Date: 28/08/2021 14:48:45
From: SCIENCE
ID: 1783602
Subject: re: Entropy Question

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

  • I rather doubt that. I’m not even convinced that it’s the right and proper SCIENTIFIC way to approach this question.
  • It may be a random process, but that’s not all it is. There need to be other factors involved.
  • Thanks. I suppose I should read that stuff as well.

(a) sure it is, from before ‘saac to beyond ‘bert great giants of scientists have relied on mathematics to transform their physics
(b) ¿ref, is there some kind of intelligent design perhaps

(a) Yes they use maths, but that’s not all they use.
(b) No implication of intelligent design. Just different types of processes.

I. but it’s still right and proper
II. well we suppose determinism is axiomatic in SCIENCE

Reply Quote

Date: 28/08/2021 15:05:49
From: The Rev Dodgson
ID: 1783614
Subject: re: Entropy Question

SCIENCE said:

The Rev Dodgson said:

SCIENCE said:

(a) sure it is, from before ‘saac to beyond ‘bert great giants of scientists have relied on mathematics to transform their physics
(b) ¿ref, is there some kind of intelligent design perhaps

(a) Yes they use maths, but that’s not all they use.
(b) No implication of intelligent design. Just different types of processes.

I. but it’s still right and proper
II. well we suppose determinism is axiomatic in SCIENCE

alpha. but is it sufficient?
beta. I’m not implying determinism either. I don’t think determinism works even if you ignore quantum mechanics stuff.

Reply Quote

Date: 28/08/2021 15:23:47
From: SCIENCE
ID: 1783622
Subject: re: Entropy Question

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

(a) Yes they use maths, but that’s not all they use.
(b) No implication of intelligent design. Just different types of processes.

I. but it’s still right and proper
II. well we suppose determinism is axiomatic in SCIENCE

alpha. but is it sufficient?
beta. I’m not implying determinism either. I don’t think determinism works even if you ignore quantum mechanics stuff.

(i) Yes, like evolution law in biology, entropy law in thermodynamics is not a scientific theory, but a mathematical theorem, videre licet statistical mechanics.
(ii) Fair enough, we reread questions and responses and appreciate that you would like us to be willing to accommodate a broader view of the idea that not only does order arise from disorder, but it reliably and persistently does so, in which case we offer the following. The above. The evolutionary ratchet known as “selection” acts upon the variation that occurs “at random” within disorder, to generate reliable and persistent order.

Disclaimer. When we say “persistent” we do not mean “forever strictly for t -> +Infinity”, similar to how when we say “foreverCOVID” we don’t mean it will still be infecting people long after humans are extinct, and similar to how when we say “zeroCOVID” we don’t mean accidents never happen despite a right and proper goal of elimination-eradication.

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Date: 28/08/2021 15:32:39
From: The Rev Dodgson
ID: 1783628
Subject: re: Entropy Question

SCIENCE said:

The Rev Dodgson said:

SCIENCE said:

I. but it’s still right and proper
II. well we suppose determinism is axiomatic in SCIENCE

alpha. but is it sufficient?
beta. I’m not implying determinism either. I don’t think determinism works even if you ignore quantum mechanics stuff.

(i) Yes, like evolution law in biology, entropy law in thermodynamics is not a scientific theory, but a mathematical theorem, videre licet statistical mechanics.
(ii) Fair enough, we reread questions and responses and appreciate that you would like us to be willing to accommodate a broader view of the idea that not only does order arise from disorder, but it reliably and persistently does so, in which case we offer the following. The above. The evolutionary ratchet known as “selection” acts upon the variation that occurs “at random” within disorder, to generate reliable and persistent order.

Disclaimer. When we say “persistent” we do not mean “forever strictly for t -> +Infinity”, similar to how when we say “foreverCOVID” we don’t mean it will still be infecting people long after humans are extinct, and similar to how when we say “zeroCOVID” we don’t mean accidents never happen despite a right and proper goal of elimination-eradication.

But will it evolve like the motion of gas particles in a sealed and perfectly insulated container, or like sand particles moving along a beach, and sorting themselves into a gradation of sizes, or like a blob of protoplasm evolving into a giraffe?

All these things could be described with maths, should you have sufficient time, but you would need much more than the law of entropy to build such a mathematical model.

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Date: 28/08/2021 15:35:49
From: SCIENCE
ID: 1783634
Subject: re: Entropy Question

The Rev Dodgson said:

SCIENCE said:

The Rev Dodgson said:

alpha. but is it sufficient?
beta. I’m not implying determinism either. I don’t think determinism works even if you ignore quantum mechanics stuff.

(i) Yes, like evolution law in biology, entropy law in thermodynamics is not a scientific theory, but a mathematical theorem, videre licet statistical mechanics.
(ii) Fair enough, we reread questions and responses and appreciate that you would like us to be willing to accommodate a broader view of the idea that not only does order arise from disorder, but it reliably and persistently does so, in which case we offer the following. The above. The evolutionary ratchet known as “selection” acts upon the variation that occurs “at random” within disorder, to generate reliable and persistent order.

Disclaimer. When we say “persistent” we do not mean “forever strictly for t -> +Infinity”, similar to how when we say “foreverCOVID” we don’t mean it will still be infecting people long after humans are extinct, and similar to how when we say “zeroCOVID” we don’t mean accidents never happen despite a right and proper goal of elimination-eradication.

But will it evolve like the motion of gas particles in a sealed and perfectly insulated container, or like sand particles moving along a beach, and sorting themselves into a gradation of sizes, or like a blob of protoplasm evolving into a giraffe?

All these things could be described with maths, should you have sufficient time, but you would need much more than the law of entropy to build such a mathematical model.

well the other fella posted about entropic gravity the other day so we leave it to them

Reply Quote

Date: 28/08/2021 16:12:42
From: transition
ID: 1783666
Subject: re: Entropy Question

The Rev Dodgson said:


transition said:

The Rev Dodgson said:

OK, I’d still like to know what TN meant by the words though.

as you were, good luck with the enterprise of convergent reality

What do you mean by “convergent reality”?

I think I’m OK with the first 7 and the 9th words.

Might come back to “enterprise” later.

neutrino is exploring what he doesn’t know, even possibly the unknowable, who knows, and credit to him for going near the unknown, the unknowable perhaps

consider the situation that yours and my neurons fire in very similar or the same patterns, regard whatever, a concept or proposition say, for the purposes of an mental representation, there are differences, and what is likely truly same shared

convergent reality might be seen as a number of things, made up of, to sketch it out, roughly, very roughly…

1. the extent they really do converge (mental representations loosely, experience of)
2. of whatever you assume or presume they do
3. the of whatever you think they should or ought
3a) the satisfactorily abstracted aspects of that
3b) the unabstracted dimension or aspects
3c) and variously the force of those above

of the force of those things, regard the assumptions and presumptions whatever does converge, and then further should or ought converge, there is some very ‘interesting’ territory, that doesn’t reliably, and universally invite a deep look, study

Reply Quote

Date: 29/08/2021 02:28:38
From: Ogmog
ID: 1783902
Subject: re: Entropy Question

Tau.Neutrino said:


Does Entropy cause complexity? If this is true then, how does order come from disorder?

Spontaneous Synchronization

The Secret of Synchronization

Reply Quote

Date: 29/08/2021 15:43:51
From: Tau.Neutrino
ID: 1784079
Subject: re: Entropy Question

The Rev Dodgson said:


Tau.Neutrino said:

Does Entropy cause complexity? If this is true then, how does order come from disorder?

What do you mean by “cause” and “complexity”?

ok, Ive read all the replies and may have mixed up my thoughts on entropy. I thought it meant something else.

The Universe is cooling down, as it does it creates galaxies and stars, planets and lifeforms, this appears to be simplicity (the singularity) moving towards complexity, (diversity of structure and life in the universe). Order appears to evolve from this. It also followers that there should be peak entropy, peak complexity, peak order and peak energy in the universe.

Can Entropy be measured, if so can we measure disorder, order, randomness and non randomness in a system.

The Universe is cooling down, where does entropy fit in this this?

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Date: 29/08/2021 15:51:33
From: Tau.Neutrino
ID: 1784087
Subject: re: Entropy Question

The Universe is cooling down, where does entropy fit in with this?

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Date: 29/08/2021 15:59:11
From: The Rev Dodgson
ID: 1784096
Subject: re: Entropy Question

Tau.Neutrino said:


The Rev Dodgson said:

Tau.Neutrino said:

Does Entropy cause complexity? If this is true then, how does order come from disorder?

What do you mean by “cause” and “complexity”?

ok, Ive read all the replies and may have mixed up my thoughts on entropy. I thought it meant something else.

The Universe is cooling down, as it does it creates galaxies and stars, planets and lifeforms, this appears to be simplicity (the singularity) moving towards complexity, (diversity of structure and life in the universe). Order appears to evolve from this. It also followers that there should be peak entropy, peak complexity, peak order and peak energy in the universe.

Can Entropy be measured, if so can we measure disorder, order, randomness and non randomness in a system.

The Universe is cooling down, where does entropy fit in this this?

The concept of entropy is indeed confusing, but increasing entropy means increasing disorder, so local increases in order are decreases in entropy, made possible by energy input, and they can’t last.

Reply Quote

Date: 29/08/2021 16:02:14
From: Tau.Neutrino
ID: 1784097
Subject: re: Entropy Question

The Rev Dodgson said:


Tau.Neutrino said:

The Rev Dodgson said:

What do you mean by “cause” and “complexity”?

ok, Ive read all the replies and may have mixed up my thoughts on entropy. I thought it meant something else.

The Universe is cooling down, as it does it creates galaxies and stars, planets and lifeforms, this appears to be simplicity (the singularity) moving towards complexity, (diversity of structure and life in the universe). Order appears to evolve from this. It also followers that there should be peak entropy, peak complexity, peak order and peak energy in the universe.

Can Entropy be measured, if so can we measure disorder, order, randomness and non randomness in a system.

The Universe is cooling down, where does entropy fit in this this?

The concept of entropy is indeed confusing, but increasing entropy means increasing disorder, so local increases in order are decreases in entropy, made possible by energy input, and they can’t last.

Ok, thanks, yes my understanding of entropy is a learning curve.

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Date: 29/08/2021 17:15:42
From: transition
ID: 1784125
Subject: re: Entropy Question

my stew is cooling, eventually the stew temperature will be the same as the room temperature, if I don’t eat it soon

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Date: 29/08/2021 17:17:22
From: Peak Warming Man
ID: 1784127
Subject: re: Entropy Question

transition said:


my stew is cooling, eventually the stew temperature will be the same as the room temperature, if I don’t eat it soon

It needs bread and butter.

Reply Quote

Date: 29/08/2021 17:20:46
From: transition
ID: 1784133
Subject: re: Entropy Question

Peak Warming Man said:


transition said:

my stew is cooling, eventually the stew temperature will be the same as the room temperature, if I don’t eat it soon

It needs bread and butter.

there’s toast under there

Reply Quote

Date: 29/08/2021 21:57:33
From: mollwollfumble
ID: 1784229
Subject: re: Entropy Question

The Rev Dodgson said:


The Rev Dodgson said:

Tau.Neutrino said:

Does Entropy cause complexity? If this is true then, how does order come from disorder?

What do you mean by “cause” and “complexity”?

And while we’re at it, the Internet says that “entropy” means:

a thermodynamic quantity representing the unavailability of a system’s thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system.

so I’ll assume that’s what you mean by it as well, unless you say otherwise.

Ya. The “complexity” is the most interesting of these definitions.

Consider for example a fluid flow. Order (eg. boundary layer flow) decays to periodic flow, which decays to chaos, which decays to randomness.
This can happen in reverse, by setting the pressure gradient, but it seldom does.

There are several ways to define complexity. From a naive point of view, the “chaos” stage is more complex than either the periodic or random stages. And that seems to be a fair way to look at it. A reduction in the complexity of chaos using either the “mathematics of strange attractors” or the “mathematics of fractals” approaches fails to match reality – sort of.

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