Introduction
“For autopoietic systems there really is no way to separate what they are from what they do.”
This is a profound observation that resonates with the free energy principle’s take on existential imperatives; namely, to exist is to be – or at least entail – a generative model of the world, embracing the fundaments of cybernetics (Conant & Ashby, Reference Conant and Ashby1970). This view speaks to mortal computation as a description of existing in a physical sense. One might ask; are there other descriptions? One candidate is statistical mechanics:
“These aspects of the free energy principle suggest that the entire edifice of active inference reaches right down into the autopoietic nature of living systems. This continuity is deepened by noting an equivalence between (minimisation of) thermodynamic free energy in metabolism and (minimisation of) variational free energy in predictive processing. … Putting all this together suggests that the (minimisation of) free energy driving metabolism, autopoiesis, and perception is not just metaphorically equivalent, but is in some physical sense is the same thing.”
This is a nice summary of how self-evidencing and thermodynamic efficiency go hand-in-hand. Technically, the above equivalence can be read as a mathematical conjugacy or, in terms of consciousness studies, a dual-aspect monism (Friston, Wiese, & Hobson, Reference Friston, Wiese and Hobson2020). The duality rests upon the fact that the internal states of anything – that are enclosed by a boundary or (Markov) blanket states – engender two information geometriesFootnote
1
. The first geometry pertains to the probability of internal states that can be read in terms of thermodynamics (Crooks, Reference Crooks2007) to which the Jarzynski equality applies (Jarzynski, Reference Jarzynski1997). In other words, thermodynamic work is required to change internal states. It is this kind of work that one measures with brain imaging. However, the free energy principle introduces a second information geometry because every internal state can be associated with a Bayesian belief about external states. This representational geometry is useful because a change in the internal states can be read as movement on a statistical manifold that corresponds to Bayesian belief updating or, in the vernacular, “changing one’s mind.” Because internal states are equipped with two information geometries, movement in one implies movement in the other. Furthermore, by construction, both share the same (free energy) minima. In fact, one can express the heat dissipated by changing the variational free energy of Bayesian beliefs as a limiting case of the Jarzynski relation. See (Friston, Reference Friston2019) for details.
Put simply, this means that there is a thermodynamic cost to belief updating or, equivalently, metabolism entails belief updating. In this setting, Landauer’s principle (Landauer, Reference Landauer1961) furnishes a lower bound on the thermodynamic work required to change one’s mind. However, this limit applies to, and only to, mortal computation; namely, the internal dynamics of mortal things. So, does it apply to universal Turing machines or immortal computation?
Mortal or immortal?
“One might argue that standard Turing computation could still simulate the mortal (or other) computations that potentially underlie consciousness in biological brains.”
The answer depends on the notion of immortal computation on Turing machines with unlimited memory and, in particular, von Neumann architectures. Von Neumann architectures require the results of computational processing to be read from – and written to – memory. Reading and writing accounts for the majority of thermodynamic work that accompanies immortal computation: see also (Fields et al., Reference Fields, Friston, Glazebrook and Levin2021). This is known as the memory wall or von Neumann bottleneck (Zou et al., Reference Zou, Xu, Chen, Yan and Han2021), which has several implications:
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• First, the bottleneck induces a Markov blanket between processors and memory. This means memory cannot realise itself, in the sense it cannot be autopoietic or self-creating.
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• Although one might argue that immortal computation (on a von Neumann architecture with unlimited memory) could simulate mortal simulation, it would not, in and of itself, be mortal. In short, it could simulate but not realise mortal computation.
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• Given that unlimited memory is (nomologically) unrealisable, the Turing–Church thesis is unrealisable, in the sense that universal computation is provably non-computable (Hutter, Reference Hutter2006).
-
• Practically, this suggests that mortal computation can only be realised with in-memory processing (a.k.a., processing in memory). Interestingly, this is a direction of travel in computer science; for example, memristor, photonic, and quantum computation (Ghose et al., Reference Ghose, Boroumand, Kim, Gomez-Luna and Mutlu2019; Zou et al., Reference Zou, Xu, Chen, Yan and Han2021).
The move towards mortal – that is, neuromorphic – computation (in the sense of in-memory processing) holds promise for approaching the Landauer limit. However, it also brings with it constraints. Specifically, it is no longer possible to upload or download memories: that is, one could not share foundation models and their functionality. This follows because mortal computation is substrate-dependent and private to the internal states of artefacts that may or may not be conscious. This suggests that consciousness – read as self-evidencing – cannot be uploaded, downloaded, or shared. Perhaps this is another bright line between intelligence and consciousness. Having said this, rapid developments in neuromorphic and in-memory processing speak to the prospect of creating conscious artefacts. The slight problem is that one will never know whether they are conscious or not:
“We humans know we’re conscious (strictly, we know it for ourselves and infer it about others).”
This simple statement may hold some deep truths. First – from the perspective of the free energy principle – one can never know whether something else is conscious or not. This follows from the fact that the only observable aspects of something are exposed on its Markov blanket (or holographic screen). This means consciousness can only be inferred, unless you are prepared to peep underneath the Markov blanket, and thereby destroy it (and, implicitly, the thing in question). The question we are left with is: could we infer “we’re conscious” without first entertaining the hypothesis that something else is conscious (i.e., you). And if not, does consciousness depend on knowing together? (i.e., having joint or common knowledge with another).
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Introduction
“For autopoietic systems there really is no way to separate what they are from what they do.”
This is a profound observation that resonates with the free energy principle’s take on existential imperatives; namely, to exist is to be – or at least entail – a generative model of the world, embracing the fundaments of cybernetics (Conant & Ashby, Reference Conant and Ashby1970). This view speaks to mortal computation as a description of existing in a physical sense. One might ask; are there other descriptions? One candidate is statistical mechanics:
“These aspects of the free energy principle suggest that the entire edifice of active inference reaches right down into the autopoietic nature of living systems. This continuity is deepened by noting an equivalence between (minimisation of) thermodynamic free energy in metabolism and (minimisation of) variational free energy in predictive processing. … Putting all this together suggests that the (minimisation of) free energy driving metabolism, autopoiesis, and perception is not just metaphorically equivalent, but is in some physical sense is the same thing.”
This is a nice summary of how self-evidencing and thermodynamic efficiency go hand-in-hand. Technically, the above equivalence can be read as a mathematical conjugacy or, in terms of consciousness studies, a dual-aspect monism (Friston, Wiese, & Hobson, Reference Friston, Wiese and Hobson2020). The duality rests upon the fact that the internal states of anything – that are enclosed by a boundary or (Markov) blanket states – engender two information geometriesFootnote 1 . The first geometry pertains to the probability of internal states that can be read in terms of thermodynamics (Crooks, Reference Crooks2007) to which the Jarzynski equality applies (Jarzynski, Reference Jarzynski1997). In other words, thermodynamic work is required to change internal states. It is this kind of work that one measures with brain imaging. However, the free energy principle introduces a second information geometry because every internal state can be associated with a Bayesian belief about external states. This representational geometry is useful because a change in the internal states can be read as movement on a statistical manifold that corresponds to Bayesian belief updating or, in the vernacular, “changing one’s mind.” Because internal states are equipped with two information geometries, movement in one implies movement in the other. Furthermore, by construction, both share the same (free energy) minima. In fact, one can express the heat dissipated by changing the variational free energy of Bayesian beliefs as a limiting case of the Jarzynski relation. See (Friston, Reference Friston2019) for details.
Put simply, this means that there is a thermodynamic cost to belief updating or, equivalently, metabolism entails belief updating. In this setting, Landauer’s principle (Landauer, Reference Landauer1961) furnishes a lower bound on the thermodynamic work required to change one’s mind. However, this limit applies to, and only to, mortal computation; namely, the internal dynamics of mortal things. So, does it apply to universal Turing machines or immortal computation?
Mortal or immortal?
“One might argue that standard Turing computation could still simulate the mortal (or other) computations that potentially underlie consciousness in biological brains.”
The answer depends on the notion of immortal computation on Turing machines with unlimited memory and, in particular, von Neumann architectures. Von Neumann architectures require the results of computational processing to be read from – and written to – memory. Reading and writing accounts for the majority of thermodynamic work that accompanies immortal computation: see also (Fields et al., Reference Fields, Friston, Glazebrook and Levin2021). This is known as the memory wall or von Neumann bottleneck (Zou et al., Reference Zou, Xu, Chen, Yan and Han2021), which has several implications:
• First, the bottleneck induces a Markov blanket between processors and memory. This means memory cannot realise itself, in the sense it cannot be autopoietic or self-creating.
• Although one might argue that immortal computation (on a von Neumann architecture with unlimited memory) could simulate mortal simulation, it would not, in and of itself, be mortal. In short, it could simulate but not realise mortal computation.
• Given that unlimited memory is (nomologically) unrealisable, the Turing–Church thesis is unrealisable, in the sense that universal computation is provably non-computable (Hutter, Reference Hutter2006).
• Practically, this suggests that mortal computation can only be realised with in-memory processing (a.k.a., processing in memory). Interestingly, this is a direction of travel in computer science; for example, memristor, photonic, and quantum computation (Ghose et al., Reference Ghose, Boroumand, Kim, Gomez-Luna and Mutlu2019; Zou et al., Reference Zou, Xu, Chen, Yan and Han2021).
The move towards mortal – that is, neuromorphic – computation (in the sense of in-memory processing) holds promise for approaching the Landauer limit. However, it also brings with it constraints. Specifically, it is no longer possible to upload or download memories: that is, one could not share foundation models and their functionality. This follows because mortal computation is substrate-dependent and private to the internal states of artefacts that may or may not be conscious. This suggests that consciousness – read as self-evidencing – cannot be uploaded, downloaded, or shared. Perhaps this is another bright line between intelligence and consciousness. Having said this, rapid developments in neuromorphic and in-memory processing speak to the prospect of creating conscious artefacts. The slight problem is that one will never know whether they are conscious or not:
“We humans know we’re conscious (strictly, we know it for ourselves and infer it about others).”
This simple statement may hold some deep truths. First – from the perspective of the free energy principle – one can never know whether something else is conscious or not. This follows from the fact that the only observable aspects of something are exposed on its Markov blanket (or holographic screen). This means consciousness can only be inferred, unless you are prepared to peep underneath the Markov blanket, and thereby destroy it (and, implicitly, the thing in question). The question we are left with is: could we infer “we’re conscious” without first entertaining the hypothesis that something else is conscious (i.e., you). And if not, does consciousness depend on knowing together? (i.e., having joint or common knowledge with another).
Financial support
This work was supported by the Wellcome Trust (KF, Ref: 226793/Z/22/Z).
Competing interests
KF serves as the chief scientific advisor for VERSES Inc.