Is there a border dividing life from non-life?

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I have always been confused over the notion of "emergence" ( I heard it used in the classroom at Cornell but it did not seem to me to signify anything real) because I have never seen in that literature an exhaustive discussion of (when or if the whole can be greater than the sum of its parts) vs (the notions where the whole is NEVER greater than a sum (no matter which) of the parts). It is clear to mathmaticians of set theory that *transitively* the w, infinite (next after all finites), IS LARGER than the sum of all finite numbers but translating this into geometry seems to have been the reason it was not applied to thoughts about emergence.

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Instead, I tend to think that algebra is here and emergence doesn't really exist, even though the cognitions you and others had associated with it in this thread did and does.

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I don't understand why you would view emergence as used here as the cardinality of a set. It is more a physical concept than a formal abstract one (at least for the time being, as it doesn't seem fully understood yet).It comes down to what you percieve to be a rational "sum" of parts. You seem to have a mathematical bent, so I'll use a set of points a1, a2..an on an (x, y) plane as an example. I'll pose two problems, one which seems to be the sum of its parts and one which seems to be greater, using that same set of points.1) What is the maximum number of lines needed to exactly bound the convex cover of any given set of a1..an points? Clearly, n (the greatest convex polygon you can make with n points). This problem does seem to be a sum of its parts; add a point, you can make an n+1-sided polygon at most.2) What is the shortest trip passing through all the a1..an points that returns to the starting point? (This is the famous travelling salesman problem, restricted to Euclidean space). You have n! possible routes (you can reduce to (n-1)! by symmetry I think, maybe even more, but you get my point); this problem is clearly NOT the sum of its parts, as adding a point multiplies the number of routes by n+1 or n, which is not additive by any stretch of the imagination.Emergence as (I think) it was used here refers to collections of simple, interacting systems exhibiting behaviours more complex than the simple intuitive 'addition' of their complexity would lead you to expect, more or less analogous to the TSP; it is not intuitively obvious (at least to me it wasn't) that a small increase in the number of points leads to such tremendous increases in the hardness of the problem.Behaviours of insect colonies, for example ants, are seen as emergent; each individual ant has a small and very simple set of behaviours (can be modeled as a finite state machine). Worker ants have a set of no more tan 40 to 80 distinct behaviours, according to E. O. Wilson (IIRC). You wouldn't expect that to 'add up' to the complex foraging, architectural and child-rearing behaviour of a colony, which seems directed by a central intelligence.The fact that these simple behaviours give rise to behaviour which seems intelligent and altogether of a different quality than the reflex behaviour of components (workers), like the architecture of Termite vent chimneys, is (or was) counterintuitive. Somewhat like the addition of a single point making the TSP much harder.The upshot of all this is that purely reductionist methods don't apply to these; looking at point subsets of the TSP doesn't seem to help you much in the solution for the whole set of points, and looking at individual ants doesn't explain the behaviour of a colony. This clashed with the reductionist worldview (IMO), and so "emergent" was probably invented to describe phenomena they intuitively never expected to be there, and which looked weird because they weren't the neat linear sum of effects which is so nice and easy to solve for.A system that behaves like the sum of its parts is statistical mechanics; you can average out velocity of particles, average out particle position, and these numbers are meaningful in understanding the whole system. Systems exhibiting emergent behaviour don't do this, they are much more immune to pure statistical analysis; a small change, insignificant statistically, CAN lead to large changes in the whole system.In essence, I think the fact that collections of ants didn't behave like collections of molecules in statistical mechanics (with obvious parameters that can be easily described and used to predict system behaviour with comparatively simple math), jarred people. Unsurprising, when you see all those early hubristic "probabilities that life originated on earth" calculations, which were basically nonsense legitimized because it was told in the math language. Instead of recognizing the hardness of assigning such a probability, let's cloak our ignorance in math and say life is extremely improbable. But I'm starting to digress.

Is this some insider joke?I have no idea what you're on about; whatever it is, it has nothing to do with what I wrote.Why do you bring inaccessible cardinals into the discussion when emergence in this context feels quite at home in finite sets, ie cellular automata? You don't even need the notion of countable infinity (at least not explicitly), and if you want to introduce it, you haven't shown me why you're using it. The fact that it's a technical term in set theory is immaterial.Why do you respond with statements about RNA to what was clearly an abstract example? Why do you assume I know who Lerner is? What does he or RNA or phenotypes have to do with what I wrote? NOTHING AT ALL. It is an abstract example, to illustrate a point about 'summing' complexity.

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>There may be a commutative sum whichthat ISNOT distributive PER >REVOLUTION(of/on/if Earth) but transient rotationally dividing >chemical classes (as if I already knew that calculation of any force >that would "flip" a Galton PolyGON.

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???

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>density dependence is a RESULT population thinking but the ability >to write the results will depend on the sample to some extent. It >may even depend on the electrons in the ant itself.

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???

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>YEs but now I would need to discuss the Galvanni-Volta, Faraday, >Gladyshev's thermostat and many things no one seems to have but in >one ear and out the ear of the other- ha!

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???

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>Thats my first go on holism versus organaciism. You'll have to give me a break, excuse the mess and make a feel @the >chance to think about it some-more.

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???I can't get over the feeling you're having me on. Few of your responses are even tangentially related to what I wrote. And all those citations of names, it looks like a satire of typical extra strong Academia-grade proof by intimidation. I don't get it.BTW, thanks ifen Why not post something I can at least understand?

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It DOES TOOOOOOOOO!!!!!!!!!!!!!!!!

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What? Honestly. I don't understand.

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I have maintained here on EVC, but perhaps you will be the first to displace this sustained attention, that while you might have ANY stat molecular distribution your good big statistical mechanical heart desires but this will not guarenttee in biology that you have a an electron DISTRIBUTION.

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Methinks you are misunderstanding my point, which was precisely about NOT always getting what our big statistical mechanical hearts desire (simplicity) in biology. I was using stat. mech. (actually thinking about the kinetic theory of gases) as an example of a system which behaves 'additively', as opposed to systems exhibiting "emergent" phenomena. Otherwise, don't know what you are talking about, and certainly made no claims about charge distributions in organisms. I'm not knowledgeable enough to discuss them. Maybe you could clarify?

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Campbell, Foundations of Science, Chance and Probability, The Theory of Chance footnote page 202 by Dover publishing... "There will, of course, be a very great change if we are considering the positions of the individual molecules, regarded as seperately identifiable. If we suppose that the molecules are not identifiable, so that all distributions are the same in which the same number of molecules is present in the same volume, then there is no change in the distribution with time. But this consideration is not relevant to our present purpose. When we say that the distribution of the molecules is dictated by chance we are thinking of the molecules as identifiable. The possiblilty of regarding certain large collections as identical although the elemetns of which they are composed are different gives rise to the study of statistics. There is a close connection between statistics and probability, but the use of statistics may be quite independent of the conceptions of chance which we are examining now."

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Now, I AM examining the unisexual salamanders. Simply try to think that the tiger salamander could not climb up on a glacier while those salamanders that did that in the past ended up reproducing ABOVE rocks their ancestors could only look up to.

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A round ringing rock my friend. If you are below it I hope you evolve.

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Again, I have no idea what you're talking about. That leap from statistical mechanics to salamanders is, I hope you'll admit, somewhat disconcerting for someone not acquainted with your thought processes.

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Because cellular automata are about fungi not lichens which you or I could engineer in some future ecosystem and besides I DID THINK of something substative in Wolfram's classifications of automata but as his own company distanced himself from it I will only now write about that under the issue of Why Weyl never got biology just left. Wolfram's "rules" and thus any cellular automata could go either way but the salamanders will always be the last play in the Bills football game (see the geographic hatching change from n-s to e-w) in the last twenty years of herpetology if you are still missing some of it) no matter how many time Gibbs had the last word.

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Sorry. I don't follow you at all. Stream-of-consciousness style does not make for clarity, you know.I'm afraid you'll have to make yourself clearer, and actually READ what I write instead of using it as a Rohrschach for your own thoughts. I think this conversation is pointless; I can't understand what argument you're putting forward. You jump around, and don't seem to realize it's incomprehensible.I don't know if you actually know what you're talking about, but if you do you should work on being able to express it. I doubt ANYONE can follow those ramblings. I don't mean to be harsh, but please understand that's no way to put forth an argument. It's like talking to an ELIZA-like program.Sorry but I can't have a conversation which I don't understand.