This is a principal world-outlook question. I think that no emergent phenomenon exists: it is enough to increase the time and space scale and, may be, the volume of the knowledges on the subject of the observation to understand that it is regular and inevitable. However, it is my philosophy, for what's it worth.

This is a principal phylosophical question. According to my vision of Nature, no truly emergent phenomenon exists: it is enough to increase the time and space scale, and, may be, our knowledge on the subject of the observation, and we will see that it is regular and inevitable. However, it is a property of my ideology.

I agree that there may be some philosophical aspect in my question but I'd like to be closer to the natural sciences like as physics, for example. I think there are lots of examples of emergent phenomena in particle physics and cosmology appearing through the course of phase transitions. One good example is the spontaneous violation of chiral symmetry of light quarks and an emergence of pions as zero modes of the new symmetry broken phase. This is just case which I started with in my question saying that emergent degrees of freedom may be built of more fundamental degrees of freedom (just as pions are composed of quarks). However, there are many other cases in phase transitions when compositeness does not play any role - in Standard Model, for example, when one goes from the symmetry phase to the Higgs phase. Anyway, let us try to go beyond the phase transition examples to find other examples, may be in biology as well. What is an emergence in general, that is the point. How would look like the emergence law - should one think, say, that there is some conservation law of degrees of freedom so that their number are always equal in fundamental and emergent stages? Or may be there works some kind of complementarity between fundamental and emergent degrees of freedom?

I am sorry for the self-advertisement, but I should write the following to support my final statement. I am the author of the original oscillation theory of catalysis and, together with Elena Kadyshevich, the author of the completely unexpected hypotheses of living-matter origination, physicochemical grounds of cellular mitosis, Solar System formation and physics of stellar transformations, and abiogenic methane origination. And I see that the theories of natural phenomena based on the statements of almost hundred-year age may be questionable. I am not sure that the today notions of the atomic nucleus structure are adequate, because they are too complicated. For example, the Bohr-Wheeler atomic nucleus model is sometimes applicable instead of the usual one. According to I. Newton, “Nature is simple and does not luxuriate in excesses”. Therefore, I am sorry again, I am not ready for discussing the specific conclusions of the theory of atomic structure without paramount necessity. Thank you for your interesting opinion. I will think about the problem formulated by you.