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What does 'emergent' mean in a physics context (split from Information Paradox)


StringJunky
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20 minutes ago, studiot said:

I think that tying down the concept is really difficult and that there are as many definitions as there are definers.

Nevertheles it can be a useful concept.

I wonder, is it in fact useful? When? Where?

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2 minutes ago, Genady said:

I wonder, is it in fact useful? When? Where?

Good point. I was thinking about it myself a moment ago. Is it really useful? Maybe thinking that a particularly difficult concept can emerge from a sub-level can be inspiring. It certainly inspired the likes of Boltzmann and Gibbs to found the statistical-mechanical version of thermodynamics, which has farther-reaching consequences than Carnot and others' version. For the most part, when people talk about this or that concept as emergent, it sounds to me either as motivational or as an afterthought.

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Posted (edited)
16 minutes ago, joigus said:

Good point. I was thinking about it myself a moment ago. Is it really useful? Maybe thinking that a particularly difficult concept can emerge from a sub-level can be inspiring. It certainly inspired the likes of Boltzmann and Gibbs to found the statistical-mechanical version of thermodynamics, which has farther-reaching consequences than Carnot and others' version. For the most part, when people talk about this or that concept as emergent, it sounds to me either as motivational or as an afterthought.

The conditions necessary seem to be: irreducible, unpredictable and novel. It is a 'useful' descriptor for those phenomena that match that criteria, otherwise, what other word(s) shall we use?

Edited by StringJunky
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A state of two quantum-entangled particles is irreducible? unpredictable? novel? emergent?

The question marks are to indicate that I'm not certain in meaning of these terms. However, I'm certain in the meaning of terms "state of two quantum-entangled particles".

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1 hour ago, joigus said:

I think @StringJunky is implying a necessary condition for a phenomenon to be emergent, not a sufficient one.

Developing the concept of necessary and sufficient sounds good to me. +1

1 hour ago, StringJunky said:

 I dunno, this concept is a work in progress for me.

A work in progress sounds good to me. +1

1 hour ago, Genady said:

I wonder, is it in fact useful? When? Where?

Good question worth exploring +1

 

1 hour ago, StringJunky said:

The conditions necessary seem to be: irreducible, unpredictable and novel. It is a 'useful' descriptor for those phenomena that match that criteria, otherwise, what other word(s) shall we use?

irreducible ? out goes Joigus' reference to elements. Nor does my arch example fit.

Unpredictable ? people have built weak arches but theya re predictable.

Novel ? Arches have been around thousands of years.

 

But perhaps arch action is not emergent.

 

As I said it is difficult and I am not offerering a definition, just trying to help.

:)

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1 hour ago, StringJunky said:

The conditions necessary seem to be: irreducible, unpredictable and novel. It is a 'useful' descriptor for those phenomena that match that criteria, otherwise, what other word(s) shall we use?

I'm not sure that these categories apply with all generality. For example: Temperature or phase transitions have been known for millenia, though they've been understood very recently. And I wouldn't hesitate to call them emergent, but never novel. Take @studiot's example of the arch, which resists a simple mathematical description, and yet the Mycenaean Greeks already used similar principles (corbelled roof) more than 3000 years ago. So it's not novel, but there is no doubt that the bricks are doing something as a 'congruence of individual behaviours' --if I may be allowed to use such mouthful-- to produce something that's not implied in their behaviour as individualities.

As to 'unpredictable'... well, it depends. Entangled states (if we allow them to be considered an example of emergence) are completely unpredictable. But the archs of the aqueduct of Segovia will be there tomorrow, I'm confident to assure.

'Irreducible' is perhaps the one that's closer to the mark, IMO. It should be understood, though, that the sense in which we say it is: Whatever these qualities (emergent) are, they're not present in the parts. If the process can be analysed, and some kind of reasoning can be applied that proves that emergent phenomenon must be the case, it should be far from obvious. Example: thermodynamics. It's very far from obvious that the thermodynamic variable that quantifies both heat and irreversible work must be related with internal degrees of freedom we cannot see directly.

I'm not sure I'm being helpful at all. It's kind of the way I understand the concept. I know it's not too far from the standard way, but there's plenty of room for nuances.

Edited by joigus
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I’d like to throw in another question - given a system consisting of a very large number of constituents which interact via known laws, is there a mathematical prescription that allows us (at least in principle) to determine all global degrees of freedom of said system from its local degrees of freedom? 

For example, could one derive Navier-Stokes equations from electromagnetism (ie H2O molecules -> water) in a purely mathematical manner? How exactly are these dynamics mapped into each other? What happens if the interaction mechanism is changed - can we predict what global effects this will have?

On a more philosophical level - are all large-scale and global degrees of freedom of the universe uniquely determined by its fundamental constituents, or is it the case that nature is actually made up of a hierarchy of laws, with each one applying to a specific length scale only, and each hierarchy being irreducible? For example, is the particle zoo of the SM the only possible choice to obtain a universe that looks like ours on large scales?

This is of practical importance, because it would mean that applying certain laws to the wrong level would be problematic. This is obvious in the down-scale direction, but we implicitly assume it’s ok to go up-scale, for example by applying GR to systems with very large numbers of constituents, and expecting the same degrees of freedom as on smaller scales.

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8 hours ago, Eise said:

... it makes no difference if a traffic jam consists of horse cards, diesel or gas cars, for a computer it makes no functional (or logical) difference if it implemented in a completely different way. ... independence of its physical substrate. No question, a physical substrate is absolutely necessary, but there are many cases where different kinds of substrates can do the job. 

This is exactly what math is -- investigation of such features which do not depend on implementation of a system. This point seems to connect back to another recent thread.

52 minutes ago, Markus Hanke said:

For example, could one derive Navier-Stokes equations from electromagnetism (ie H2O molecules -> water) in a purely mathematical manner?

Perhaps, Navier-Stokes equations are not derivable from the molecular level, but a system behavior that these equations describe is. As if we had a gigantic computer which could simulate evolution of a system of billions molecules of water, a macroscopic behavior of water would appear in the output.

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Posted (edited)

Found an interesting view in Nature: Defining emergence in physics. It notes the disparity between the biological and physics views on the subject. It seems that a physics definition needs infinities to comply, according to them,  whereas biology needs a very large but finite number. The authors propose this as a working physics definition:

Quote

Clearly, no single definition of emergence can encompass all the uses that the word has enjoyed. Here we discuss a sharp definition of the narrow concept of emergence in physics; we give a mathematically precise meaning to the notion of ‘qualitative difference.’ We propose the following:

An emergent behavior of a physical system is a qualitative property that can only occur in the limit that the number of microscopic constituents tends to infinity.

https://www.nature.com/articles/npjquantmats201624

Edited by StringJunky
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9 hours ago, Genady said:

 

Perhaps, Navier-Stokes equations are not derivable from the molecular level, but a system behavior that these equations describe is. As if we had a gigantic computer which could simulate evolution of a system of billions molecules of water, a macroscopic behavior of water would appear in the output.

The Navier Stokes equations are readily derivable equations connecting perfectly well defined mathematical entities.
However they are non linear and as such have only few known particular solutions in simple cases. We do not have a general solution, although the existence and uniqueness theorem suggests there must be one.
That is why there is a prize offered for a general solution.

2 hours ago, StringJunky said:

Found an interesting view in Nature: Defining emergence in physics. It notes the disparity between the biological and physics views on the subject. It seems that a physics definition needs infinities to comply, according to them,  whereas biology needs a very large but finite number. The authors propose this as a working physics definition:

https://www.nature.com/articles/npjquantmats201624

Well I can't go with this definition, since it rules out my arch. But it is an interesting proposal and admittedly narrow.

@joigus and I seem to be dancing around one characteristic that you have named 'novel'. Thank you for your explanation of that use of novel. I agree but suggest that by itself novel is too brief as others have read it differently.
Your Nature article also acknowledges the problem of including a time factor in any definition.
The one characteristic is the idea of a large number of parts/components/elements combining in some way  to produce the emergent effect as a result. The Nature articles implies this can only happen with an infinite count. I hold that the number need not even be large, let alone infinite, although it could be.

Going back to my arch consider the following thought experiment (which is actually possible in practice).

Take a bunch of wooden bricks (I say wooden because ceramic ones could break during the experiment).
Toss them up into the air to land in a jumbled heap.
Sooner or later a few of these will land in the configuration of an imperfect arch.
Further trials will bring better and better arches.

So the 'emergence' of an arch configuration has a statistical dependance. The probability of a perfect arch is very small, one in a very large (perhaps infinite) number.

Chemical reaction dynamics has a similar statistical dependence. The rate of a reaction product being formed depends upon the probabilities of the right configuration of the right molecules occurring.
Unlike the arch, we do not know the right configuration or the right molecules for the formation of Life, so we cannot substantiate the hypothesis that Life is an emergent phenomenon that occurred this way.

It is worth noting that in the case of the arch we know both the right elements and the right configuration so we can deliberately construct an arch, ie change the probabilities to approach certainty.

So I would like to propose a modification to @Eise proposal that instead of saying it does not matter what the elements the phenomenon emerges from, to certain formative elements must be present and correctly configured,  but it does not matter how they themselves arise or arrive.

Edited by studiot
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The fact that sometimes you need infinitely-many degrees of freedom, or perhaps, a large enough number is not essential, IMO for qualitatively different features to appear. Examples:

1) The 2-body problem in celestial mechanics is always solvable, the 3-body problem is always chaotic (because the equations are non-linear from the get-go.

2) An entangled system of 2 identical particles displays correlations that a 1-particle system cannot reproduce, because it violates Bell's inequality.

And I agree with Studiot that the Navier-Stokes equation is quite transparent as to its meaning. It's consistent with the conservation of mass (continuity equation), conservation of angular momentum, energy, etc. So the behaviour of the constituents is apparent in the form of the equation, yet there are consequences of the equation (turbulent regimes, and so on) that have no correlate to the behaviour of one particle.

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When I read,

12 hours ago, Markus Hanke said:

I’d like to throw in another question -

I was bracing myself.

And then...,

12 hours ago, Markus Hanke said:

given a system consisting of a very large number of constituents which interact via known laws, is there a mathematical prescription that allows us (at least in principle) to determine all global degrees of freedom of said system from its local degrees of freedom? 

 

And I only have this to say: I think that largely depends on the system, and the laws being dealt with.

I really don't think it's possible to establish the terms for emergence to occur in a completely unambiguous way. Let alone given that physicists and biologists, as StringJunky noticed, do not completely agree on what's required.

In the context of physics in particular, I'm familiar with the following difficulty that I've pointed out before on a related thread, and that's due to Leonard Susskind, AFAIK:

When we reach a fundamental level of description, what is 'the system' and what are 'the parts' is not even clear. I remember the examples Susskind used were bosonization (a fundamental fermion can be considered as a couple of bosons with a kink between them = a twist in space-time) and dualities in QFT (a theory in a certain limit looks very much like another theory when we consider different limits).

(Not a literal quote; rather, my re-phrasing of the observation.)

Edited by joigus
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In philosophy, emergence usually is defined in terms of two classes, weak and strong.  

From SEP:

Though diverse, accounts of ontological emergence can be usefully grouped by a basic division between those that are and are not compatible with physicalism, understood as the thesis that all natural phenomena are wholly constituted and completely metaphysically determined by fundamental physical phenomena. This thesis is standardly understood to entail “the causal closure of the physical”, according to which (roughly) any fundamental-level physical effect has a purely fundamental physical cause. “Strong” emergence accounts are inconsistent with physicalism and causal closure (as just elucidated) while weak emergence accounts are consistent with it.

https://plato.stanford.edu/entries/properties-emergent/

My sense of these terms is that weak emergence lies in observations like "water is wet." Though we cannot easily deduce wetness from a single H20 molecule, it seems possible in principle to get there from fundamental physical causes.  The loose joinery of molecules, the latent heat of vaporization, etc.  Some theorists believe that there are some phenomena, like consciousness, volition, or spacetime, which require strong emergentism in which higher-level functions take on unique and fundamental causal powers which micro-constituents do not have.  It seems to me that this more robust definition of emergence is where the controversy is thickest.

Many emergent phenomena are simply our macro level experience of them, and do not really provide any reason to imagine special macro level causal powers.  

 

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41 minutes ago, TheVat said:

My sense of these terms is that weak emergence lies in observations like "water is wet." Though we cannot easily deduce wetness from a single H20 molecule, it seems possible in principle to get there from fundamental physical causes.  The loose joinery of molecules, the latent heat of vaporization, etc.

Wow I'm completely blown away by this completely incorrect statement from a recognised authority.

Wet, Wetting and Wetness and molecules are precisely defined terms in the physical sciences which arise from surface tension effects.
Since ST arises from differential interactions between at least five molecules and wetting between at least two of these, ascribing any wetness to a single molecule is nonsense.

Incidentally I prefer to use two words rather than strong and weak plus one word (which actually inefficiently makes three words to learn) for different concepts.

So I use emergent and arising.

Edited by studiot
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Two points:

You are picking at an example while missing the conceptual point of defining weak emergence.  If the example has technical problems, fine, whatever.  Did you bother to read the SEP article?  

Second, "recognized authority"??  WTF is this rude snarkiness about?  Did someone piss in your oatmeal?  I am not a chemist, nor have made such claims.  If deriving wetness from micro-constituents doesn't work for you, then just pick another example.  Gas pressure, tornadoes, whatever floats your boat, brother.  If there is some secret grudge thing here, just PM me, okay?  Otherwise, back the fuck off and lose the attitude.

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1 hour ago, TheVat said:

Two points:

 

Second, "recognized authority"??  WTF is this rude snarkiness about?  Did someone piss in your oatmeal?  I am not a chemist, nor have made such claims.  If deriving wetness from micro-constituents doesn't work for you, then just pick another example.  Gas pressure, tornadoes, whatever floats your boat, brother.  If there is some secret grudge thing here, just PM me, okay?  Otherwise, back the fuck off and lose the attitude.

Wow ?

Is this an example civility left over from your defunct forum ?

You referenced the Stanford Encyclopedia of Philosophy, to which I pay a subscription.

2 hours ago, TheVat said:

 

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Studiot:

It's a response to your rudeness, calling my example of water is wet as from a "recognized authority.". It seemed directed at me, given that those were my words and not a quote from SEP.  The example was mine.  You brought the incivility and the blowback is what you got.

The fact that you took my example with extreme literalness (yes of freaking course you would need a handful of molecules to understand interactions and bonding) in order to nitpick at that rather than address the main point of the example, suggested you simply wanted something to pick on.  

 

And strong and weak emergence are the terms generally used in philosophy of science, and in particular disciplines where they are at issue.  The fact that you pay a subscription (for a website that has no paywall) is nice, but has zero relevance to the topic.  

I hope the definition of types of emergence was useful to other members, who have more open minds.

PS - Looking back at my post, I note the quote from SEP was in a different font, followed by the URL.  Which was then followed by my own comments.  Clearly indicated with a different font.  

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Allegedly, communication breakdown due to mutual misinterpretation of terms and implied meanings and responses thereof can be a good example of an emergent phenomenon. ;) I beseech you both to come back to good terms ASAP.

We all value both of you.

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16 minutes ago, StringJunky said:

Looks like TheVat misinterpreted Studiot's post.

Thank you.

I also realise another characteristic of emergence I haven't mentioned.

If you some bricks, you can build some sort of structure, even if just a pile.

But unless you have enough bricks you cannot build an arch.

In other words, the emergent phenomenon only emerges when all the necessary precursors are in place.

The change from no emergence to emergent is sudden.

This is consistent with the link to Catastrophe theory I referred to earlier in the thread.

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58 minutes ago, joigus said:

Allegedly, communication breakdown due to mutual misinterpretation of terms and implied meanings and responses thereof can be a good example of an emergent phenomenon. ;) I beseech you both to come back to good terms ASAP.

We all value both of you.

Thanks, I did go back and take note of where the mutual misunderstood parts were.  Oddly flattering that anyone would think my writing would be worthy of the SEP.  Anyway, I see the snark was unintended, so I'm sorry for misunderstanding. Carry on.   

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22 hours ago, Genady said:

As if we had a gigantic computer which could simulate evolution of a system of billions molecules of water, a macroscopic behavior of water would appear in the output.

Well, this is what we assume (of course with good reason) would happen - but how can we show this?

11 hours ago, joigus said:

When we reach a fundamental level of description, what is 'the system' and what are 'the parts' is not even clear.

Good point.

10 hours ago, TheVat said:

the causal closure of the physical”, according to which (roughly) any fundamental-level physical effect has a purely fundamental physical cause

Ok, but who is to say that “fundamental” necessarily has to be absolute and global? My thoughts were that ‘fundamental’ might be scale-dependent, so that laws can form a hierarchy, wherein each set of laws is fundamental on that level. So basically fundamental to me would mean irreducible. In that picture, nature would come about as a set of strata, ie a multi-level hierarchy of laws, each one of which being irreducible. Each lower level would then form a boundary condition of the next higher level, but does not uniquely determine it.

This is not a claim - I don’t necessarily believe that nature is like this. I am simply speculating out loud, to see what implications emergence might have.

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Posted (edited)
9 hours ago, studiot said:

Thank you.

I also realise another characteristic of emergence I haven't mentioned.

If you some bricks, you can build some sort of structure, even if just a pile.

But unless you have enough bricks you cannot build an arch.

In other words, the emergent phenomenon only emerges when all the necessary precursors are in place.

The change from no emergence to emergent is sudden.

This is consistent with the link to Catastrophe theory I referred to earlier in the thread.

Yes, I'll go with those. The sudden part is where I implied jokingly  'magic'... it just seems to appear.

Edited by StringJunky
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1 hour ago, Markus Hanke said:

Well, this is what we assume (of course with good reason) would happen - but how can we show this?

G: ... if we had a gigantic computer which could simulate evolution of a system of billions molecules of water, a macroscopic behavior of water would appear in the output.

M: Well, this is what we assume (of course with good reason) would happen - but how can we show this?

G: By building such a simulation, or an approximation, and let it run. There is a very successful computer simulation of the Universe evolution, with creation of filaments, voids, super clusters and such, with 2.1  trillion “particles” in a space of 9.6 billion light-years across for more than 13 billion years.

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