Information

2nd axiom & postulate of IIT

Summary 

Information is an essential property of experience (an axiom) and, by inference, also an essential property of the substrate of consciousness (a postulate). 

The axiom states that experience is specific: it is this one. Formulated in physical terms, the postulate states that the cause–effect power of the substrate of consciousness must be specific: it must be in this state and select this cause–effect state. 

Information Axiom

Experience is specific: it is this one.

[This excerpt is taken from Tononi, G. (forthcoming). On Being.
Ch. 2: The axioms of phenomenal existence.] 

No matter what my experience might be—pure blackness and silence before I open my eyes, or, once I open them, the bright blueness outside the window, or the sight of my body on the bed in my room—my experience is always a specific one, this one. What would it even mean to have a generic experience? To see a color that is not black or blue, but generic? A description of an experience may be generic, yet the experience itself is always specific [1]. And the experience I am having is specifically this one rather than another one—it is always the specific one it is. 

Because an experience is always this specific one, it also differs from a large repertoire of other possible experiences, each of which is also specific, as illustrated in the figure. The availability of this repertoire is called differentiation [2]. 

Information is immediate, in the sense that I do not have to infer that an experience is this one: the experience I am having is the one “right here, in front of my eyes.” Information is also irrefutable, in the sense that its negation is self-contradictory or absurd. Think of having an experience that were not “this one.” I cannot conceive of an experience that were not the one it is, but generic. And while I can conceive that my experience could be some other one—”that one”—when I experience it, it would be “this one,” reaffirming the validity of the axiom. Finally, specificity is true not just of the experience I am having now, but it must be true of every conceivable experience—every experience must be “this one” when I experience it. Therefore, information is another essential property of phenomenal existence.

Footnotes

[1] Note that “generic” as opposed to “specific” (or “determinate”) is different from “general” as opposed to “particular” [...].[2] Unlike information (“an experience is this specific one”), differentiation (“it is one out of many possible experiences”) is not axiomatic because it depends on the assumption that there are other possible experiences. It is conceivable that there could be no other experiences besides the one I am having: my momentary experience right now may have “come out of nowhere” and may immediately “go back to nowhere.” 

Information Postulate

The cause–effect power of the substrate of consciousness must be specific: it must be in this state and select this cause–effect state. 

[This excerpt is taken from Tononi, G. (forthcoming). On Being.
Ch. 3: The postulates of physical existence I.]

Phenomenally, information means that every experience is specific—it is this one—rather than being generic or being a different one. In physical terms, this means that the substrate must be in a specific state (this state) and “select” a specific cause state and a specific effect state over itself (this cause–effect state). The specific state the substrate is currently in—which units are ON and which are OFF—is established by observation. In the case illustrated in the figure below, the current state is Abcd [1]. The specific cause and effect state are established by considering the column (inputs) and row (outputs) of the substrate TPM corresponding to its current state (red column and green row).

The current state has several possible causes (input states that increase its probability above chance) and several possible effects (output states whose probability it increases above chance). To determine which of these the system selects, we follow the principle of maximal existence. The principle states that, when it comes to a requirement for existence, what exists is what exists the most. In the case of information, the substrate selects the cause for which it takes the most difference from itself (its maximal or intrinsic cause) and the effect for which it makes the most difference to itself (its maximal or intrinsic effect).

In the figure, the substrate selects cause state aBcd and effect state abCd (indicated by the red and green squares on the TPM, respectively). Together, they make up the specific, intrinsic cause–effect state aBcd–abCd. Operationally, the cause–effect state is determined by evaluating intrinsic information (ii) for all possible cause and effect states and selecting the intrinsic cause and effect for which ii is maximal—the state that is maximally informative intrinsically [2]. For the example substrate state Abcd, the maximal ii on the cause side is 2.58 (iic*), corresponding to aBcd, and on the effect side it is 3.01 (iie*), corresponding to abCd.

Information Postulate - 08/2023

Intrinsic information measures the specific cause–effect power from the intrinsic perspective of a system in its current state and is defined as the product of informativeness and selectivity [3]. Informativeness can be thought of as the “raw power” of the substrate in its current state over a cause or effect state: it captures existence (cause–effect power) as well as intrinsicality (cause-effect power of the substrate over itself). For example, on the effect side, informativeness is high if the probability of an effect state given the current state is far above its average probability given all possible current states (corresponding to chance).

Selectivity, in turn, can be thought of as the substrate’s “control” over a cause or effect state, which is high if their probability given the current state is close to certainty. The selectivity factor also captures the intrinsicality postulate. For example, on the effect side, selectivity ensures that effect power depends not only on how much a system in its current state increases the probability of an effect state compared to chance (“raw power”), but also on how close that probability is to certainty (“control”). This is because, from the intrinsic perspective of the system, any uncertainty about whether it would produce a specific effect (a reduction in its probability compared to certainty) “dilutes” its effect power.

To maximize intrinsic information, informativeness and selectivity—raw power and control—must both be high. It also follows that intrinsic information is sensitive to a tension between expansion and dilution [4].

The cause–effect state that maximizes intrinsic information can be thought of as substrate’s “best bet” about its cause and effect from its intrinsic perspective in its current state. But the intrinsic cause and effect are potential causes and effects: they may or may not actually occur, depending on extrinsic circumstances [5, 6].

In the information axiom, we saw that as a consequence of being specific, every experience differs from a large repertoire of other possible experiences. This property of differentiation applies for the postulate as well. Depending on its current state among a repertoire of possible current states, the substrate of consciousness may specify a different cause–effect state among a repertoire of possible cause–effect states. This is illustrated in [the figure above] by the two smaller brains, each of which has a different substrate state and a different cause–effect state.

Note that the notion of information captured by the information postulate is different from that employed in communication theory. Information in IIT is causal rather than merely observational. It is intrinsic to a system, rather than relative to an observer that assesses it across a channel. And it is specific, requiring a specific cause and effect within a repertoire of potential alternatives, rather than being assessed as an average [see FAQ: How is information in IIT different from “Shannon information”?]. 

[To see how the information postulate is operationalized mathematically, see Computing Φ, Step 3: Compute intrinsic information.] 

Footnotes

[1] Uppercase italics indicates ON and lowercase italics OFF.[2] Strictly speaking, the information postulate alone only defines a candidate intrinsic cause (or effect). A true intrinsic cause (or effect) must also comply with the postulates of integration and exclusion—it must be maximally irreducible, within a maximally irreducible complex, as discussed in the following sections.[3] The value of intrinsic information for the maximal cause or effect state corresponds to the intrinsic difference—the only difference measure that satisfies the three postulates of existence, intrinsicality, and information (Barbosa et al. 2020).[4] In particular, due to intrinsicality (the requirement to take the intrinsic perspective), the system cannot exploit an “extrinsic” perspective to select its cause–effect states. For example, it cannot exploit extrinsic knowledge and treat some units as informative and others as noisy, or take advantage of previous occurrences to help in the selection of its current cause–effect state (the way, say, engineers can use error-correcting codes in communication channels). [5] Actual causation (“what causes what”) can be quantified by employing IIT’s postulates in an extrinsic context, as shown in (Albantakis et al. 2019).[6] Similarities and dissimilarities with Bayesian inference are discussed in Marshall et al., in preparation.

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For the information axiom, please cite Tononi, Giulio. Forthcoming. On Being. Chapter 2: The axioms of phenomenal existence.For the information postulate, please cite Tononi, Giulio. Forthcoming. On Being. Chapter 3: The postulates of physical existence I.