It is commonly taken, that complex functioning networks can be either chaotic or ordered, but not simultaneously. Also, that life is on the edge of chaos. It is true for random networks, and was investigated for Boolean, autonomous networks, mainly by Kauffman for RBN (Random Boolean Network). Chaos and order are taken as variants in stability aspect. However, living objects are not random, especially in aspect of stability, because just for this property are selected by natural selection [2011eng.1.13; 2014eng.1.14; 2017-21eng.1.21; 2020eng.2.15; 2016pl.3.10;]. Kauffman’s conclusion, that life is on the edge of chaos and order in RBN, where there is phase transition between chaos and order, is correct, but this effect and model is a large simplification. Other effects in less simplified models are much more stronger.

I have shown in [2017-21eng.1.21; 2020eng.2.15; 2016pl.3.10;] that third state (I call it half-chaos)of networks exists, but it is for not fully random networks. This state much better describes living objects, than edge of chaos of random networks. It allows to use for modeling (especially of living objects) higher connectivity as is estimated from reality, and more signal variants as I have shown [2011eng.1.13;] that is needed for adequate statistical investigations.

Already in [2014eng.1.14;] I have shown one example of network with ‘chaotic parameters’, which is not random in one aspect: it has point attractor, and this is enough for strange property: such network is simultaneously chaotic and ordered, when small permanent disturbances are imposed. Using such network for modeling of living object is much more correct – there is a death, which is needed for elimination in the mechanism of natural selection. Without of natural selection there is no life [2008eng.1.5; 2010eng.1.12; 2013pl.3.3;  2014pl.3.4; 2016pl.3.10;].

To explain this thesis and its subversibility we must start from notion of ‘purposeful information’. It is open (disclosed) and exact name of ‘biological information’. Purposefulness is treated as dangerous term and typically omitted, but this way a correct understanding is omitted. My theory is lack of finalism error, it is correctly teleonomic and a goal is not based on an intention.

The best, known to me definition of biological information was given by Eva Jablonka (2002). Biological information has three aspects: Shannon’s one, and ‘teleo-semantic’. Teleonomic and semantic stay not satisfactorily described. I propose exact theory of information and purposeful information in [2008eng.1.5; 2010eng.1.12; 2009eng.1.8; 2013pl.3.3;], which contain all of these aspects.

Shannon discusses information exchange, but before describing the exchange, he defines what will be exchanged (transmitted). I take this as information. It must not be transmitted. However, typically it is taken, that information exists only, where it is transmitted – in such a case it is not an ‘information’ but ‘informing’.  I take information as a choice only in a set of available choices. Next, this choice may be mapped into a second set of other possibilities. It is a coding, which indicates in the new set a ‘symbol’ of choice in the first set. Meaning of the symbol is the choice in the first set. To get this meaning we must decode symbol into element of first set. The code may be natural if transformation from first to second set is created by physical lows. Such transformation describes determinism, where first information is a cause, and its symbol is an effect. Decoding of natural code is searching of a cause for assumed effect. Such effect, for which cause is searched, we typically call ‘purpose’. I calla record of the connection of a cause with indicated effect a ‘purposeful information’. This theory is described in [2008eng.1.5; 2010eng.1.12; 2009eng.1.8; 2013pl.3.3;] and now the book is written about it. Typically, for natural code, the reverse natural code does not exist and such decoding must be created by an universal construction (Universal decoder) which uses existing natural code. Such construction tests hypothesis.

Next I ask: can purposeful information accumulate itself autonomously? Investigating this question I found, that it can appear only if a goal is ‘continuation of existence’. Properties of such process are so similar to life process, that it should be taken as definition of life process. The main mechanism (above construction) for the above goal is just the Darwinian one. This process does not have any goal, the above goal is an element of such mechanisms, it is not defined outside of process. Descriptions of this theory can be found also in Polish in [2013pl.3.3;   2014pl.3.4;   2015pl.3.6;  2016pl.3.10;]. Half-chaos adds for life definition deep base of natural identity and death (elimination) of evolving object. It practically creates Darwinian natural selection and other form of life definition as process of random changeability that saves half-chaotic state.  

Haeckel's 'recapitulation of phylogeny in ontogeny' is now treated as the old false conception - this theme is closed and should not be reanimated(Wilkins 2002). However, this conclusion is based on false deduction and it is the greatest scandal in the science. This empirical regularity loses its explanation, when heredity of acquired characters appear false. Explanation is not a base. Naive (from current point of view with complex networks) attempts of new explanation based on ‘the only base for biology – genetics’ fail. It was concluded, that recapitulation cannot have such an explanation, means - is false. From [1975eng.2.1; ] and later [2005eng.1.2; 2005eng.1.3; 2008eng.1.4; 2009eng.1.7;] I try to show, that explanation exists, but it is based on statistical structural tendencies in adaptive evolution of complex networks. Such a base was totally ignored by biologists. All my investigation leads to prove my explanation of recapitulation, but on the way I have few hills to defeat: 1- in the biology the theme is closed but outside is not known; 2 – I assume for my simulation that life is in the chaos (has parameters like fully random system that is chaotic), what is currently in opposite to Kauffman’s hypothesis ‘life on the edge of chaos and order’. I am just overcoming this second hill by discovery of half-chaos (see [thesis1a] [2011eng.1.13; 2014eng.1.14; 2017-21eng.1.21; 2020eng.2.15; 2016pl.3.10;]).