I hope Dr Fernando E. Rosas writes a book for non-technical people someday. All of his research topics are super interesting and it would be cool to have him explain how they're connected in his mind in a way that's more accessible.
I mostly agree with you, but I would add that systems fit different models (aka abstractions) as they scale and that as we add water molecules to a system we'll start to see microfluidic, then fluid, then oceanographic,.. cosmological properties emerge. The molecules are the same and always behaved with all of those properties, but whether or not we can see them easily, or can use them as a modelling tool depends on the scale.
I've began to question the complexity of many of these paradoxes I run into these days.
In this case, isn't this just a matter of the definition of a "heap of sand"? The article seems to sort of forget to define a heap and just proceeds to make a problem out of it and asking questions like "when does a heap become not a heap?" when it was never even defined why would we call something a heap in the first place.
So I think the real question there is just that why are you calling something a heap in the first place and when you have an answer to that, that same answer will also help you with figuring out when the thing you call a heap is not a heap anymore.
> when it was never even defined why would we call something a heap in the first place.
Cultural conditioning, technically, "just [the] reality", "you know what I mean", etc colloquially. It's a broadly "known" meaning, despite no definition, that's where the paradox comes from.
Lots of things are like this, the requirement(!) to fight wars for example - there's no objective definition for why we must do it, we just "know" that we must. And if you disagree with me, just ask anyone and see what they say (watch out though, quite often people will trick you and answer both yes and no to the same question, with complete sincerity).
Watch children playing house and listen carefully to how they talk, how they describe the details of their imaginary world, etc....its an innate feature of human consciousness, it never goes away, but it becomes cloaked by education, culture, "facts", etc.
You're totally right, and this exactly the sort of thing Wittgenstein set out to show. The trouble is that people have an idea of what a "heap" is and what "evil" is and what "knowledge" is and a lot of philosophy is concerned with pinning down those notions or at least saying something concrete about them.
I think the Sorites paradox may point to something specific about these kinds of ideas, which is not shared with the meaning of things like evil or knowledge. There's a page on it on SEP: https://plato.stanford.edu/entries/sorites-paradox/
The problem is that heap has only an informal connotative definition, not a denotative one. 4 grains of sand doesn't seem like a heap, but if your kid leaves 4 of his toys out you might consider it a heap.
So now what, does the definition of a heap have to account for the subject's and object's relative scales? Formalizing informal notions is not always straightforward.
I've only skimmed the paper so far, but apart from both using the word "emergence" I think you and the paper are talking about very different things. The paper means something along the lines of "behaviours at different scales that are causally isolated from each other", and they give a mathematical treatment of that.
I imagine they would agree with you that there's nothing magical about it! The map is not the territory but some maps are better than others.
Yes, nothing magical about it, but the macro behaviour is only possible with "enough" of the micro behaviour in some cases.
You can, for example, go mathematically from describing individual behavior to describing macro behaviour and see the macro emerging in the limit (e.g., homogenization of PDEs).
I don't know if I disagree with this, but this reminded me about one thing that for some reason stuck to my mind once.
It was about statistics and probabilities. I think I was talking with ChatGPT about superpositions or something and somehow we got to talking about how e.g it might be impossible to make a system which could predict everyone's favourite flavour of ice cream.
Interestingly enough though, it is perfectly possible to gather data about people's favourite ice cream flavours (and we could even go as far as to say that we could ask every single human on the planet) and make a statistical model which is able to answer what is most probably everyone's favourite ice cream flavour.
I find this really interesting. We could think of one person's flavour as essentially random and impossible to predict, but when we gather enough of these random data points, we are for some reason able to build a relatively accurate system to guess someone's favourite flavour. I don't think this is obvious at all.
Anyway, I didn't have any real point here. I just wanted to share one example of interesting thing that I think is an example of "emergent behaviour" and seemingly magical at that too.
I've always thought of emergence as "a behavior at scale which is unintuitive or difficult to predict given understanding of a lesser scale".
More specifically, I think "emergence" is more about the blind spots we have as meat calculators than something magical, unless you ascribe to the notion of "magic" as "something sufficiently advanced or complex as to be difficult to understand", in which case I think actually yeah, emergence is magical behavior from that perspective.
I don’t have enough brain jam to spread on this systems stuff these days, but it seems to me that they’re ignoring the dynamics of the way these software systems operate within and around human social systems. Are they just seeking to describe a mathemagical model to predict the behaviour of a complicated system (ie. a 747), rather than a truly complex one (ie. mayonnaise)?
I didn’t get far enough to establish whether they had identified that each software system is not mathematically predictable, given they they will always (usually) be deployed, designed or behave differently, as a reflection of some human requirement (e.g. cost, ergonomics, supportability, speed, etc). That - to me anyway - is what makes technical systems-of-systems truly ‘complex’, as opposed to a series of complicated but entirely deterministic binary formulas.
I skim through it rapidly, but the paper seems interested in building a framework for finding out if and when a microstate participates in the outcome of the macrostate, or if the macrostate dynamics can be evaluated without looking at the microstate.
That is, given a time series Z observed as a function of another time series X (what is called in the paper coarse-graining function), past values of Z are enough to establish causal connections with future values, without knowing X.
Thanks - I'm familiar with systems theories, but I wanted to understand whether anyone got far enough into the paper to determine whether they had covered the aspects mentioned in my post.
My read is that the computational dynamics involved in a microstate cause it to map into a stable macrostate over time. Proving that the microstates map to the macrostates is the real trick. This implies the microscopic level is computing the state of information on the macroscopic level. It seems like 'strong lumpability' means the microstate mappings are equivalent to a macrostate, so we can safely infer the dynamics of a system based on the macrostate without having to compute from the microstate.
From the paper: "causally closed levels can be efficiently controlled from just macroscopic interventions,
without needing to intervene on microscopic conditions."
I think that's stating things causally rather than predictively but two sides of the same coin.
I agree though. One issue the paper doesn't seem to underscore or delineate are the roles of measurement or intervention costs (in an information or utility theoretic sense) at different levels of emergence and how those affect decisions to work at one level or another.
25 comments
[ 1.1 ms ] story [ 77.1 ms ] threadThe thing is that we use different (and incompatible) abstractions to describe processes in differing contexts.
The map is not the territory.
I mostly agree with you, but I would add that systems fit different models (aka abstractions) as they scale and that as we add water molecules to a system we'll start to see microfluidic, then fluid, then oceanographic,.. cosmological properties emerge. The molecules are the same and always behaved with all of those properties, but whether or not we can see them easily, or can use them as a modelling tool depends on the scale.
In this case, isn't this just a matter of the definition of a "heap of sand"? The article seems to sort of forget to define a heap and just proceeds to make a problem out of it and asking questions like "when does a heap become not a heap?" when it was never even defined why would we call something a heap in the first place.
So I think the real question there is just that why are you calling something a heap in the first place and when you have an answer to that, that same answer will also help you with figuring out when the thing you call a heap is not a heap anymore.
Cultural conditioning, technically, "just [the] reality", "you know what I mean", etc colloquially. It's a broadly "known" meaning, despite no definition, that's where the paradox comes from.
Lots of things are like this, the requirement(!) to fight wars for example - there's no objective definition for why we must do it, we just "know" that we must. And if you disagree with me, just ask anyone and see what they say (watch out though, quite often people will trick you and answer both yes and no to the same question, with complete sincerity).
Watch children playing house and listen carefully to how they talk, how they describe the details of their imaginary world, etc....its an innate feature of human consciousness, it never goes away, but it becomes cloaked by education, culture, "facts", etc.
So now what, does the definition of a heap have to account for the subject's and object's relative scales? Formalizing informal notions is not always straightforward.
I imagine they would agree with you that there's nothing magical about it! The map is not the territory but some maps are better than others.
You can, for example, go mathematically from describing individual behavior to describing macro behaviour and see the macro emerging in the limit (e.g., homogenization of PDEs).
It was about statistics and probabilities. I think I was talking with ChatGPT about superpositions or something and somehow we got to talking about how e.g it might be impossible to make a system which could predict everyone's favourite flavour of ice cream.
Interestingly enough though, it is perfectly possible to gather data about people's favourite ice cream flavours (and we could even go as far as to say that we could ask every single human on the planet) and make a statistical model which is able to answer what is most probably everyone's favourite ice cream flavour.
I find this really interesting. We could think of one person's flavour as essentially random and impossible to predict, but when we gather enough of these random data points, we are for some reason able to build a relatively accurate system to guess someone's favourite flavour. I don't think this is obvious at all.
Anyway, I didn't have any real point here. I just wanted to share one example of interesting thing that I think is an example of "emergent behaviour" and seemingly magical at that too.
More specifically, I think "emergence" is more about the blind spots we have as meat calculators than something magical, unless you ascribe to the notion of "magic" as "something sufficiently advanced or complex as to be difficult to understand", in which case I think actually yeah, emergence is magical behavior from that perspective.
> My take on this is that there is no "emergence" that appears when grouping elements together into a larger system.
I didn’t get far enough to establish whether they had identified that each software system is not mathematically predictable, given they they will always (usually) be deployed, designed or behave differently, as a reflection of some human requirement (e.g. cost, ergonomics, supportability, speed, etc). That - to me anyway - is what makes technical systems-of-systems truly ‘complex’, as opposed to a series of complicated but entirely deterministic binary formulas.
This paper isn't exactly, you know, light reading.
That is, given a time series Z observed as a function of another time series X (what is called in the paper coarse-graining function), past values of Z are enough to establish causal connections with future values, without knowing X.
This is what I understood, at least.
https://en.wikipedia.org/wiki/Complexity_theory
in particular;
https://en.wikipedia.org/wiki/Complex_systems
https://en.wikipedia.org/wiki/Assembly_theory
https://en.wikipedia.org/wiki/Complex_adaptive_system
[1]: https://www.wolframphysics.org/
I think that's stating things causally rather than predictively but two sides of the same coin.
I agree though. One issue the paper doesn't seem to underscore or delineate are the roles of measurement or intervention costs (in an information or utility theoretic sense) at different levels of emergence and how those affect decisions to work at one level or another.