Jan Tilden 9:33am, 3 January 2008
Am I right in thinking that when we talk about emergence, we need something to be going on that is perceivable to us as some sort of pattern or structure at one hierarchical level, while that which causes it is at a lower hierarchical level and necessarily "blind" to that which emerges? So in the case of the emergence of flock behaviour, birds are just doing what birds do, keeping distance etc and that produces the pattern we call flock behaviour. In other words the birds aren't trying to act like a flock and are not aware in any sense that they are acting like a flock. There is nothing like a "group mind" at work.

Similarly, with the lichen on the rock, living cells are just doing what cells do and the shape of the plaque that we call "a lichen" emerges. It's not destined in any teleological way to be a lichen, that's just a consequence of activity that's going on, willy nilly, at another hierarchical level.

It seems to me that perception (and perhaps even human perception) is critical to identifying emergence. We have to perceive some structure, some pattern that has the kind of hierarchical relationship described above with a set of processes producing that structure or pattern.

All this makes me wonder, what is the relationship between mathematics and emergence? Is mathematics an emergent product of the human mind? Or is it the very thing that underlies all emergence, in that there is no emergence without pattern and no pattern without mathematical properties? Or are they one and the same?
resolute condition [deleted] Posted 14 years ago. Edited by resolute condition (member) 14 years ago
I'd like to say something about perception. I think we will be able to find the most reliable and consensual answer for the linking problem between maths and emergence when all identifiable points of view were boarded properly.

I talked to a friend of mine about this some months ago. She's a psychoanalyst and said that it's impossible tot it's impossible to know the truth about something or to know truly and fully the object of investigation. This is because the human being, when something comes to his knowledge, he automatically interprets it with his own perception e recreates the object in his mind. This object is not the true object, but one copy of the original. It's a interpretation of the real object and not the true object.

If we cannot know truly the object, it's impossible to know something. What we have is only an idea of the real world, not the knowledge of the real world.

With this evidence, we can imagine if we are able to see hidden things underneath every object or simply miss them.
Maths is a human interpretation about events. We may see Maths everywhere in our world, but its rules are not valid out of here.

Emergence is something beyond our capability to perceive. There will always be links between emergence and all Science, all fruits of our interpretation. The truth will never be perceived fully, as all possible knowledge will never be reached fully.
whiteoakart 14 years ago
I agree with your idea of perception, arthursteinn. However, we must be careful not to dwell on this too much, or nothing has any meaning or substance to us. When we talk about "knowing" something, we are really talking about the things we can infer from repeatable observations. This is a scientific concept. The concept you propose is really a philosophical one.

Regarding mathematics, math doesn't really exist as a separate thing. It is really a language of sorts that helps us define the natural world. This is why we run into weirdness like negative square roots. What we can learn with mathematics are the patterns and algorithms of the natural world. Then we can make reliable predictions.

jan~n- I agree with your idea of emergence as non-teleological. However, your statement "that perception (and perhaps even human perception) is critical to identifying emergence" is self-referential. That is, the very act of identification implies and requires a sentient perception. So I am not exactly sure what you are getting at.

However, emergence exists with or without perception. It is an outcome of natural processes. Our perception of it simply gives it a name.

Jan Tilden Posted 14 years ago. Edited by Jan Tilden (member) 14 years ago
I guess I'm trying to get at what emergence is beyond perception, since as you say, emergence exists whether or not we give it a name. I've just been back to the Wikipedia definition and find that the debate I'm starting is already ongoing in emergence theory and it is by no means decided whether emergence exists beyond human perception.

The relevant section in the wiki article is headed "Objective or subjective quality" and I'm taking the same position as that of Crutchfield who says that "Defining structure and detecting the emergence of complexity in nature are inherently subjective, though essential, scientific activities." He goes on to say that our ability to see emergence depends on our computational ability and that is exactly what I'm getting at when I say that there is "no emergence without pattern and no pattern without mathematical properties."

On the other hand, I'm confident David would agree with Corning "Must the synergies be perceived/observed in order to qualify as emergent effects, as some theorists claim? Most emphatically not. The synergies associated with emergence are real and measurable, even if nobody is there to observe them."

So would you say that the patterns exist as a separate thing but the mathematics does not? I think Crutchfiled would say that patterns are nothing but our ability to perceive with mathematical brains.

Does this make it clearer why I'm interested in the relationship of mathematics to emergence?
whiteoakart 14 years ago
jan~n wrote: Does this make it clearer why I'm interested in the relationship of mathematics to emergence?

David: OK, I see what you mean. I am going to have to think about this. I will read the wiki and post some kind of reply.

Can I restate the problem:
Does the definition of emergence include the pattern and/or the synergies? And, if including the pattern is necessary to the definition, does a pattern exist outside of computational perception, or is it an artifact of perception?
Jan Tilden Posted 14 years ago. Edited by Jan Tilden (member) 14 years ago
I agree with this restatement except I would use the word "product" rather than "artifact" of perception. Strictly speaking I don't think it's possible to get outside of perception to know what is artifactual and what is "real".
kugel 14 years ago
The description by arthursteinn about perception and emergence is very interesting, and may be the way to tackle the topic of this discussion. However, mathematics is not a perception, but is a human interpretation about events, as arthursteinn says.

On my opinion, mathematics is simply a natural science which serves only as an instrument for interpreting nature, or to facilitate the interpretation of other natural sciences, i.e. physics, or to describe less natural behaviors, i.e. finance and stock market. Now, let me be provocative. There is nothing emergent from mathematics, it only provides a rigorous basis for defining and demonstrating emergence (see Wikipedia).

It is true that there are wierd features, i.e. the Moebius string, or the impossible Escher geometry, or square roots of negative numbers or immaginary numbers - as whiteoakart points out - which human mind can hardly figure out. However, even immaginary numbers have their role, i.e. by describing the solutions for an harmonic oscillator (in terms of a second order linear differential equation) . All the feautres in mathematics are a tool for the interpretation or description of (natural) events. This concept reflects more or less Descartes line of reasoning.
resolute condition [deleted] 14 years ago
Everything related to natural science is always complicated to refuse or to establish new statements, as natural science comes to give us a explanation concrete and with the necessary logical substance to make us understand something "natural" about the study's object.

Natural science is basic and we always base our thoughts and discoveries on this. So, how to question natural statements and established rules about the natural world without hanging to natural science? It’s still impossible in our scientific way of discovery. Natural science provides us the path to discover things we haven’t noticed before.

So, the relation between this path and Emergence is just that this is our path to discover things in or about Emergence. There may be other ways to think and discover but we human beings are like to think about everything based on natural science.

As our perception is tainted with the natural science way of view to discover, we will always see links between natural science and everything, mainly Emergence. If there is or not Mathematics in Emergence is the same as ask ourselves if there is colour on objects or not, as colour is just our perception about the object.
Jan Tilden 14 years ago
In reply to Kugel's latest post.

Quoting Arthursteinn, Kugel says: "However, mathematics is not a perception, but is a human interpretation about events"

Assuming that "interpretation" means processing information in such a way that what comes out is not the same as what went in, all perception involves interpretation. This process starts at the level of the sense organ itself and continues throughout the perceptual train. If mathematics is (albeit unconsciously) involved in that interpretation then mathematics is part of perception.

Kugel also says: "There is nothing emergent from mathematics, it only provides a rigorous basis for defining and demonstrating emergence"

I'm not so sure about this. It might be true but I'd like some opinions on the following:

(a) At this web address is a link to a paper by Slovak physicist Metod Saniga. If you download the pdf you will see some beautiful patterns that have "fallen out" of his mathematical explorations in projective geometry. As yet, these are not connected with anything in the "real world" though I know Saniga thinks they will be. I don't understand any of this mathematics but this looks to me like an example of emergence and Saniga himself describes it thus: "The lecture introduced and discussed novel, and rather unexpected, properties of the fine structure of the projective lines defined over finite rings, which emerged as a by-product of our recent applications of these remarkable geometries in quantum physics."

(b) Einstein said that his theory of relativity sprang from mathematics. He didn't have the theory then do the maths, the theory fell out of (emerged from?) the maths. His finding had many implications at the level of the "real world" and we are still exploring them.

(c) James Clerk Maxwell discovered radio waves purely by doing mathematics. He was trying to understand the relationship between electricity and magnetism. He didn't start with a theory, but a set of mathematical tools. To me, it seems like the electromagnetic spectrum, including the existence of the, till then, undiscovered radio waves emerged from his mathematics. In this case the pattern that emerged was quickly connected with something in the "real" world.

So my question is, are these examples of emergence? And if not, what is missing from them that makes them not qualify as emergence?
resolute condition [deleted] Posted 14 years ago. Edited by resolute condition (member) 14 years ago
Answering jan-n about those examples, all the obvious examples about emergence are connected with the "real world". But it's just simple examples. There are infinite examples varying since simple to more complicated ones, remembering the "Cartesian Method of Descartes", which tells us that we need to begin with simple things to understand complex things.

Philosophy is not always connected physically to the "real world" but ideally (metaphysically). For instance, the discussion firstly initiated by my master Max Weber about the "Axiological Neutrality in Social Sciences" in an example of how we can discuss subjects related ideally to the “real world”.

Considering this, there is emergence in simple examples and complex examples. There are also ideally examples of emergence, ones that are not physically connected to the “real world” but ideally, like those examples gave by Jan-n. Those examples did not emerge from Mathematics, they were perceived by the Mathematic way of view of discovery. There are Emergence examples in all sciences and examples out of our science, as out of the conditions that propitiates the life we know as possible including ours, our rules are no longer valid, our science is no longer valid, a perception that open our eyes to one world completely different to our conception of truth, logic and concrete, showing us that Emergence can or cannot be connected to our science, more than that, can be something beyond our possibility to know.

There will never be Emergence without certain conditions that make possible the event of Emergence. Emergence does not happen alone as all natural science does not exist alone.

In “a”, the Emergence discovered mathematically is connected with Quantum Physics and Geometry. This Emergence is not only mathematical but also physical and all sciences that we can connect with or not, remembering what we do not know about;

In “b”, the Emergence discovered by Einstein is also related to other sciences. But the difference is that he went further, showing that our science is primitive to explore those events.

In”c”, the Emergence discovered mathematically is related to Magnetism and Electricity.

We will always perceive Emergence with scientific eyes, hanging to Mathematics, Physics or Philosophy, but Emergence will always include more than one scientific event.
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