Updated: Jan 2
The more complex an information source state is, the more (existentially) statistically unlikely it is. The same goes for sources. The Shannonian definition of a source is a stochastic physical process (Ben-Naim, 2017; Shannon, 2001; Weaver, 1949). Thus, all information sources necessarily reduce to spatiotemporal dynamic structure (or else strongly supervene upon it.) Moreover, the less structure, and the less structural complexity and heterogeneity (especially functional-structural heterogeneity) a source, or source-set (set of sources), has, the less intrinsic information it has. Always.
Note that the structural complexity mentioned cannot be random, or randomness. Information rich structure is natural-kind heterogeneous in its ontic basis, but also in its spatiotemporal arrangement, or configuration. Randomness is like entropy – the more random an information source is, the more uniform and unstructured it is. In other words, maximally random spatiotemporal structure is minimally structurally heterogeneous, and minimally informational.
(I will not spill ink on it here, but the nature of structure itself is a matter of intense debate among mathematicians and philosophers of science. (Arenhart & Bueno, 2015; Beni, 2016, 2020; Berenstain & Ladyman, 2012; Brading & Skiles, 2012; Bueno, 2008, 2010, 2018; Chakravartty, 2012, 2004; Cruse, 2005; Don Ross, 2008; Doppelt, 2014; Esfeld & Lam, 2011; Esfeld, 2013, 2017; Floridi, 2008; French & Ladyman, 2011; Frigg & Votsis, 2011; Gerard & Ball State University, 2009; Kallfelz, 2013; Krause, 2005; Ladyman, 2011; Lam & Wüthrich, 2015; Long, 2014; Lyre, 2011; Mccabe, 2006; Morganti, 2004, 2011, 2018; Psillos & service), 2009; Psillos, 2001; Psilos, 2005; Saatsi, 2010; Saunders, 2003; Schmidt, 2010; “Structural realism,” 2016; Votsis, 2012; Wang, 2008).)
You can test these facts easily from the armchair if you know enough simple, basic, hard science. The most complex entity known to us is the human brain and CNS-PNS (central nervous system and peripheral nervous system) coupling. These might end up superseded by quantum computing based AI and extremely complex software simulations. However, in terms of natural-kind-heterogeneous structure, we are not there yet. Probably (Boston Dynamics might have something they are not telling us about!) Brains are relatively common on Earth, but they are extremely uncommon in the universe (especially good ones!)
What the universe has plenty of is empty space (the quantum vacuum) and things like gas clouds, dust, and rocks. The measure of information (by any measure) in any of those not-brain things is tiny compared to the measure of information in any given human brain (even the ones that aren't so sharp!)
Gas clouds, dust, and the vacuum (which contains EMS energy and radiation) have comparatively little natural kind heterogeneity, and comparatively homogeneous and random structure. They are structurally, and indeed functionally, vastly simpler than brains. (In fact in many cases they cannot be considered to be functional in any coherent sense). This is true even for enormous cosmological and celestial bodies. Jupiter and the crab nebula might both be vastly larger than all of the human brains combined (all of the human brains that ever existed, combined, in fact): but their complexity from the perspective of both natural kind heterogeneity, structural complexity, and evolved teleo-functional informational potential (functions with some kind of apparent purpose): they’re much less complex than even one human brain (Deacon, 2007, 2010, 2011; Green, 2013; Logan, 2012; Pietarinen, 2012).
Even high school students know that Jupiter will not be painting you anything any time soon, nor exhibiting circadian rhythms, nor possessing and enacting introspection. It simply does not have any information sources that are structurally and functionally type-heterogeneous and complex enough. Even chaotic systems do not.
If an advanced alien species sent you plans for a time machine in their equivalent of a solid-state thumb drive, the gate logic of the memory might be comparatively simple (it might look like something Stanley Kubrick would put in his movie), but the information laid down and stored in it would be a very different story: exceedingly complex in terms of informational heterogeneity and functional heterogeneity.
There is more (by any information measure) heterogeneous-structure-based information in your brain (I am in a generous mood) than in all the rocks, gas clouds, nebulae, and lifeless planets. Certainly this is so if one includes functional information: information source sets that have very high complex functional-state potential, or can produce very large numbers of informationally different, and informationally dependent, operational or teleological functions and mechanisms. Simply stated, there is a lot more information where there is more complex, and especially complex teleonomic, structure and function.
Doubtful? Again – it is easy to prove from the armchair with basic hard scientific concepts and understanding. How many things, of any kind, that do not have a brain can have emotion, build rockets, or paint? For that matter: how many can cry when they are hungry, let alone form a visual representation of potential food? They do not have what it takes informationally speaking, because they do not have what it takes in terms of natural-kind structural, and functional, heterogeneous information sources. They are not the right kind of information sources, or physical processes, in any important structural respect. Information processing reduces to physical processes, always. (Philosophers should not so readily doubt Rolf Landauer, who said that there is no information without physical representation, and that information is a physical entity. (DiVincenzo & Loss, 1998; R Landauer, 1961; Rolf Landauer, 1991, 1996, 1999; Sagawa & Ueda, 2009)).
Complex (including by MDL and compression-based measures), very informationally heterogeneous sources and source states are rare: they are statistically unlikely according to frequentism, and also by classical, and Bayesian, probability theory. The best explanation for their existence is that they must evolve over time, and indeed that is what the evidence (in vitro population experiments, genetics, and the fossil record) tells us about all complex, replicating, organismic information sources of all kinds.
All complex, organismic information sources we know of – without exception - have long histories of accumulating informational and functional complexity. They can not instantaneously, nor even quickly, become complex lifeforms, with complex, adapted, teleological functions. There is good reason to adduce – based upon apparently universal nomic constraints and laws of nature – that our epistemic access to such systems provides a sound indication of universal objective reality. The statistical likelihood of a swampman brain – a brain produced instantaneously by lightning hitting a swampy gas cloud and zapping a full human with a brain into existence – is so near to zero as to be effectively impossible (C Adami, Ofria, & Collier, 2000; Christoph Adami, 2002; Antony et al., 1996; Arendt & Schleich, 2009; Bayés et al., 2017; Corning & Szathmáry, 2015; Eccles, 1994; Escudeiro et al., 2019; V. M. Eskov, Eskov, Vochmina, Gorbunov, & Ilyashenko, 2017; V. V. Eskov, Filatova, Gavrilenko, & Gorbunov, 2017; Galas, Nykter, Carter, Price, & Shmulevich, 2010; Hintze & Adami, 2008; Lenski, Ofria, Pennock, & Adami, 2003; McShea, 2017; Mesoudi, 2016; Millikan, 2010; Nandi, Bhadra, Sumana, Deshpande, & Gadagkar, 2013; Pattee, 2012; Petto & Mead, 2008; Read & Andersson, 2019; Takeuchi & Hogeweg, 2008; Pontarotti, 2017; Wu & Nan, 2019; Yaeger, 2014).
As information sources, all self-organising, or autopoietic, self-replicating, organismic, complex systems are structurally very heterogeneous. The heterogeneity is both spatiotemporal, modular, and natural kind based. Such systems have a high number of functional processes and modules, or modular mechanisms, with a high level of informational interaction and interdependence (information rich and information dependent, including signal and transmission rich). They also have a high density and degree of natural kind heterogeneity, which is increased by their heterogeneous modular functions (the modules, and the functions, are both heterogeneous). Brains are the most complex of such organismic systems.
Anything with introspective intelligence has neurology as a necessary condition. We do not know of any alternatives yet. Artificial intelligence is a product of our brains, which are currently a necessary condition for its existence. AI is also necessarily coming to fruition only over relatively long timescales, and with the application of much directed effort and energy. There are no examples of any such entity that did not evolve over very long timescales.
Invoking some kind of highly intelligent designer - apart from adaptive evolution - is not a coherent explanation for the existence of informationally dense and complex organisms like brains. At minimum there is a regress to deal with. However, there are even more difficult informational complexity problems to deal with.
The regress could only be allayed by using evolutionary explanations. Such a designer would have to have at least the same informational complexity as human brains. If one existed (if it could even be characterised as an individual), the only explanation that would be not only scientifically - but informationally - sound, would be a cosmological evolutionary explanation according to which informational density could emerge along with evolved heterogeneous complexity. The more complex the mind-brain equivalent possessed by the designer, the less statistical chance - diminishing to zero - that they could be a Davidsonian swampman that did not emerge over a long period of time by evolutionary selectional, cumulative, and adaptive, processes. Even in a vast universe, they are simply not going to instantaneously materialise as a complex set of teleonomic, functional information sources. That kind of instantaneous and non-evolved informational density and complexity in a source, and in source states, is diminishingly improbable.
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