Intelligence as information processing: brains, swarms, and computers

There is no agreed definition of intelligence, so it is problematic to simply ask whether brains, swarms, computers, or other systems are intelligent or not. To compare the potential intelligence exhibited by different cognitive systems, I use the common approach used by artificial intelligence and artificial life: Instead of studying the substrate of systems, let us focus on their organization. This organization can be measured with information. Thus, I apply an informationist epistemology to describe cognitive systems, including brains and computers. This allows me to frame the usefulness and limitations of the brain-computer analogy in different contexts. I also use this perspective to discuss the evolution and ecology of intelligence.


INTRODUCTION
In the 1850s, an English newspaper described the growing global telegraph network as a "nervous system 12 of the planet" (Gleick, 2011). Notice that this was half a century before Santiago Ramón y Cajal (1899) 13 first published his studies on neurons. Still, metaphors have been used since antiquity to describe and try can be useful for different purposes (Gershenson, 2004). For example, in the 1980s, the debate 25 between symbolists/representationists (brain as processing symbols) (Fodor and Pylyshyn, 1988) and 26 connectionists (brain as network of simple units) (Smolensky, 1988) did not end with a "winner" and 27 a "loser", as both metaphors (computational, by the way) are useful in different contexts. 28 There have been several other metaphors used to describe cognition, minds, and brains, each with their 29 advantages and disadvantages (Varela et al., 1991;Steels and Brooks, 1995;Clark and Chalmers, 1998; to studying cognition. Nevertheless, all of these metaphors can be described in terms of information 34 processing. Since computation can be understood as the transformation of information (Gershenson,35 2012), "computers", broadly understood as machines that process information can be a useful metaphor 36 to contain and compare other metaphors. Note that the concept of "machine" (and thus computer) could 37 also be updated (Bongard and Levin, 2021). 38 Formally, computation was defined by Turing (1937 As many have noted, the continuous nature of cognition seems to be closely related to that of the living 47 (Maturana and Varela, 1980;Hopfield, 1994;Stewart, 1995;Walker, 2014). We have previously studied 48 the "living as information processing" (Farnsworth et al., 2013), not only at the organism level, but at all 49 relevant scales. Thus, it is natural to use a similar approach to describe intelligence.

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In the next section, I present a general notion of information and its limits to study intelligence. Then, 51 I present the advantages of studying intelligence in terms of information processing. Intelligence is not 52 restricted to brains, and swarms are a classic example of this, which can also be described as information 53 processing systems. Before concluding, I exploit the metaphor of "intelligence as information processing" 54 to understand its evolution and ecology.  Shannon (1948) proposed a measure of information in the context of telecommunications, that is 56 equivalent to Boltzmann-Gibbs entropy. This measure characterizes how much a receiver "learns" 57 from incoming symbols (usually bits) of a string, based on the probability distribution of previously 58 known/received symbols: if new bits can be completely determined from the past (as in a string 59 with only one repeating symbol), then they carry zero information (because we know that the 60 new symbols will be the same as previous ones). If previous information is useless to predict the 61 next bit (as in a random coin toss), then the bit will carry maximum information. Elaborating 62 on this, Shannon calculated how much redundancy is required to reliably transmit a message 63 over an unreliable (noisy) channel. Even when Shannon's purpose was very specific, the use of 64 This is a provisional file, not the final typeset article 2

Gershenson
Intelligence as information processing information in various disciplines has exploded in recent decades (Haken, 1988;Wheeler, 1990 . 71 We can say that electronic computers process information explicitly, as we can analyze each change 72 of state and information is encoded in a precise physical location. However, humans and other animals 73 process information implicitly. For example, we say we have memories, but these are not physically at a 74 specific location. And it seems unfeasible to represent precisely the how information changes in our brains.

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Still, we do process information, as we can describe "inputs" (perceptions) and "outputs" (actions). 76 Shannon assumed that the meaning of a message was agreed previously between emitter and receiver.

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This was no major problem for telecommunications. However, in other contexts, meaning is not a trivial 78 matter. Following Wittgenstein (1999), we can say that the meaning of information is given by the use 79 agents make of it. This has several implications. One is that we can change meaning without changing 80 information (passive information transformation (Gershenson, 2012)). Another is the limits on artificial 81 intelligence (Searle, 1980;Mitchell, 2019), as the use of information in artificial systems tends to be 82 predefined. Algorithms can "recognize" traffic lights or cats in an image, as they are trained for this 83 specific purpose. But the "meaning" for computer programs is predefined, i.e. what we want the program 84 to do. The quest for an "artificial general intelligence" that would go beyond this limit has produced not 85 much more than speculations.

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Even if we could simulate in a digital computer all the neurons, molecules, or even elementary particles 87 from a brain, such a simulation would not yield something akin to a mind. On the one hand, interactions 88 generate novel information at multiple scales. On the other hand, as mentioned above, observers can give 89 different meanings to the same information. In other words, the same "brain state" could refer to different 90 "mental state" for different people. In a sense, this is related to the failure of Laplace's daemon: even with 91 full information of the states of the components of a system, prediction is limited because interactions 92 generate novel information (Gershenson, 2013a). And this novel information can determine the future 93 production of information at different scales through upward or downward causation (Campbell, 1974; 94 Bitbol, 2012; Flack, 2017), so all relevant scales should be considered (Gershenson, 2021a).

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In spite of all its limitations, the computer metaphor can be useful in a particular way. First, the limits on 96 prediction by interactions are related to computational irreducibility (Wolfram, 2002). Second, describing 97 brains and minds in terms of information allows us to avoid dualisms. Thus, it becomes natural to use 98 information processing to describe intelligence and its evolution. Finally, information can contain other 99 metaphors and formalisms, so it can be used to compare them and also to exploit their benefits.

INTELLIGENCE
There are several definitions of intelligence, but not a single one that is agreed upon. We have similar more. These concepts could be said to be of the type "I know it when I see it", to quote Potter Stewart.

Intelligence as information processing
Still, having no agreed definition is no motive nor excuse for not studying a phenomenon. Moreover, 105 having different definitions for the same phenomenon can give us broader insights than if we stick to a 106 single, narrow, inflexible definition.

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Thus, we could define intelligence as "the art of getting away with it" (Arturo Frappé), or "the ability 108 to hold two opposed ideas in mind at the same time and still retain the ability to function. One should, 109 for example, be able to see that things are hopeless and yet be determined to make them otherwise" 110 (F. Scott Fitzgerald). Alan Turing (1950) proposed his famous test to decide whether a machine was 111 intelligent. Generalizing Turing's test, Mario Lagunez suggested that in order to decide whether a system 112 was intelligent, first, the system has to perform an action. Then, an observer has to judge whether the 113 action was intelligent or not, according to some criteria. In this sense, there is no intrinsically intelligent 114 behavior. All actions and decisions are contextual (Gershenson, 2002). Like with meaning, the same 115 action can be intelligent or not, depending on the context and on the judge and their expectations.

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Generalizing, we can define intelligence in terms of information processing: An agent a can be described 117 as intelligent if it transforms information (individual (internal) or environmental (external)) to increase its 118 "satisfaction" σ.

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I have previously defined satisfaction σ ∈ [0, 1] as the degree to which the goals of an agent have been 120 fulfilled (Gershenson, 2007(Gershenson, , 2011b. Certainly, we still require an observer, since we are the ones who 121 define the goals of an agent, its boundaries, its scale, and thus, its satisfaction. Examples of goals are 122 sustainability, survival, happiness, power, control, and understanding. All of these can be described as 123 information propagation (Gershenson, 2012): In this context, an intelligent agent will propagate its own 124 information.

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Brains by themselves cannot propagate. But species of animals with brains tend to propagate. In this 126 context, brains are parts of agents that help process information in order to propagate those agents. From 127 this abstract perspective, we can see that such ability is not restricted to brains (Levin and Dennett, 2020).

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Thus, there are other mechanisms capable of producing intelligent behavior.

SWARMS
There has been much work related to collective intelligence and cognition (Hutchins, 1995 scalability of information processing of brains is much superior than that of swarms.

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Thus, the brain as computer metaphor is not appropriate for studying collective intelligence in general, 142 nor swarm intelligence in particular. However, the intelligence of brains and swarms can be described in 143 terms of information processing, as an agent a can be an organism or a colony, with its own satisfaction σ 144 defined by an external observer.

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This is a provisional file, not the final typeset article 4

Intelligence as information processing
Another advantage of studying intelligence as information processing is that we can use the same 146 formalism to study intelligence at multiple scales: cellular, multicellular, collective/social, and cultural.

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Curiously, at the global scale, the brain metaphor has also been used (

EVOLUTION AND ECOLOGY
If we want to have a better understanding of intelligence, we must study how it came to evolve. Intelligence 150 as information-processing can also be useful in this context, as different substrates and mechanisms can 151 be used to exhibit intelligent behavior.

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What could be the ecological pressures that promote the evolution of intelligence? Since environments 153 and ecosystems can also be described in terms of information, we can say that more complex environments 154 will promote -through natural selection -more complex organisms and species, which will require a 155 more complex intelligence to process the information of their environment and of other organisms and 156 species they interact with (Gershenson, 2012). In this way, the complexity of ecosystems can also be 157 expected to increase though evolution.

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These ideas generalize Dunbar's (1993; 2003) "social brain hypothesis": larger and more complex social 159 groups put a selective pressure on more complex information processing (measured as the neocortex to 160 bodymass ratio), which gives individuals more cognitive capacities to recognize different individuals, 161 remember who can they trust, multiple levels of intentionality (Dennett, 1989), and so on. In turn, 162 increased cognitive abilities lead to more complex groups, so this cycle reinforces the selection for more 163 intelligent individuals.

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One can make a similar argument using environments instead of social groups: more complex 165 ecosystems put a selective pressure for more intelligent organisms, social groups, and species; as they 166 require greater information-processing capabilities to survive and exploit their environments. This also 167 creates a feedback, where more complex information processing by organisms, groups, and species 168 produce more complex ecosystems.

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However, individuals can "offload" their information processing to their group or environment, leading its cost imposes limits that depend as well on the usefulness of increased cognitive abilities.

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Generalizing, we can say that information evolves to have greater control over its own production 174 (Gershenson, 2012). This leads to more complex information-processing, and thus, we can expect 175 intelligence to increase at multiple scales through evolution, independently on the substrates that actually 176 do the information processing.

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Another way of describing the same: information is transformed by different causes. This generates 178 a variety of complexity (Ashby, 1956;Gershenson, 2015). More complex information requires more 179 complex agents to propagate it, leading to an increase of complexity and intelligence through evolution.

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At different scales, since the Big Bang, we have seen an increase of information processing through 181 evolution. In recent decades, this increase has been supraexponential in computers (Schaller, 1997).

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Although there are limitations for sustaining this rate of increase (Shalf, 2020), we can say that the 183 increase of intelligence is a natural tendency of evolution, be it of brains, swarms, or machines. This 184 will not lead to a "singularity", but to an increase of the intelligence and complexity of humans, machines, 185 and the ecosystems we create.

Gershenson
Intelligence as information processing

CONCLUSION
Brains are not essential for intelligence. Plants, swarms, bacterial colonies, robots, societies, and more 187 exhibit intelligence without brains. An understanding of intelligence (and life ) 188 independently of its substrate, in terms of information processing, will be more illuminating that focussing 189 only on the mechanisms used by vertebrates and other animals. In this sense, the metaphor of the brain as 190 a computer, is limited more on the side of the brain than on the side of the computer. Brains do process 191 information to exhibit intelligence, but there are several other mechanisms that also process information 192 to exhibit intelligence. Brains are just a particular case, and we can learn a lot from them, but we will 193 learn more if we do not limit our studies to their particular type of cognition.

CONFLICT OF INTEREST STATEMENT
The authors declare that the research was conducted in the absence of any commercial or financial 195 relationships that could be construed as a potential conflict of interest.

AUTHOR CONTRIBUTIONS
C.G. conceived and wrote the paper.

FUNDING
This work was supported by UNAM's PAPIIT IN107919 and IV100120 grants.