Dissociating Artificial Intelligence from Artificial Consciousness

• Explanation of Constraints: Non-Overlapping and Non-Mediation: Figure 10 explains some fundamental rules that define 'intrinsic units' within Integrated Information Theory (IIT). Intrinsic units are the building blocks of a system that has cause-effect power, a key concept in IIT related to consciousness. Panel A illustrates the constraint of non-overlapping units. It shows two units, α and β. These units cannot share any underlying components. This is because if they did, we would be counting the same cause-effect power multiple times. To assess their cause-effect power, we need to be able to manipulate each unit independently and observe the results. Panel B illustrates that a unit within a complex cannot act as a mediator, or go-between, for other units in the same complex. In other words, if unit 'a' influences unit 'c', and unit 'b' is in between, then 'b' cannot be considered an intrinsic unit of the same complex as 'a' and 'c'. All of a's influence on c must be accounted for by b's cause-effect power.
• Explanation of key terms: The figure uses the terms 'causal marginalization,' 'observation,' and 'manipulation.' 'Manipulation' refers to setting the state of a unit directly. 'Observation' refers to simply noting the state of a unit. 'Causal marginalization' is a technical term in IIT that refers to averaging over all possible states of a unit, weighted by their probabilities. It's a way of removing a unit's influence to see what remains.

• Fundamental postulates of IIT: The constraints illustrated in the figure are fundamental postulates of IIT. They are essential for ensuring that cause-effect power is properly quantified and that the identified intrinsic units are indeed irreducible and non-overlapping.
• Accurate visual representation: The figure accurately represents these constraints in a simplified, visual manner, making them easier to understand.

• Clear and effective visual representation: The figure uses simple diagrams and clear labels to illustrate the constraints on intrinsic units within the framework of Integrated Information Theory (IIT). The use of distinct panels (A and B) to represent different constraints is effective. The distinction between 'observation', 'manipulation' and 'causal marginalization' is well presented.
• Caption could be more descriptive; lack of explicit reference in main text: The caption is concise, but could be slightly more descriptive. The figure is not explicitly referenced in the main text, which might make it difficult for readers to fully appreciate its significance without carefully reading the supplementary material.

• System Description and Rule 110: Figure 11 introduces a different four-unit system called WXYZ, which, unlike the previous PQRS system, follows a specific rule known as "Rule 110" from the field of elementary cellular automata. Panel A shows the four units (W, X, Y, Z) and their connections. Each unit's next state depends on its own current state and the states of its immediate neighbors. Panel B presents this rule in two ways: a truth table and a transition probability matrix. Both show all possible combinations of the four units' states and their corresponding next states. It is called an elementary cellular automaton because each cell (or unit) only has two possible states and updates based on simple, local rules. Panel C and D show the application of IIT analysis to the system, resulting in cause-effect structures. Panel C shows that the system can be broken down into two complexes: WZ and y. Panel D shows the unfolded cause-effect structures.
• Significance of Rule 110: Rule 110 is significant because it has been proven to be Turing-complete. This means that, in principle, it can perform any computation that any other computer can, given enough time and space.

• Accurate representation of Rule 110: The representation of WXYZ as an elementary cellular automaton implementing Rule 110 is accurate and consistent with established definitions in the field. The truth table and transition probability matrix correctly reflect the rule's dynamics.
• Validity of IIT analysis: The application of IIT analysis to WXYZ, as shown in panels C and D, is methodologically sound within the context of the paper's theoretical framework.

• Comprehensive but could improve clarity in panel A: The figure presents a four-cell elementary cellular automaton (WXYZ) and its dynamics. The use of multiple panels (A, B, C, D, E) to show different aspects (system diagram, truth table, transition probability matrix, and cause-effect structures) is effective for a comprehensive presentation. However, panel A could benefit from explicitly labeling the inputs to each cell, as this is crucial for understanding how Rule 110 is applied.
• Clear caption: The caption clearly states what the figure represents. The use of 'Rule 110' might require prior knowledge, but the figure itself provides the necessary information to understand the rule.

• Detailed Labeled Diagram of the Computer: Figure 12 presents the same four-bit computer as shown in Figure 2, but this time with all of its 117 individual components, or units, clearly labeled. These labels (like P₁, P₂, R₁, etc.) allow for precise identification of each component within the computer's architecture. The computer is organized into distinct functional modules: the clock and frequency dividers (which control the timing of operations), the program and instruction register (which store the instructions for the simulation), the data registers and buffer (which store the current state of the simulated system), and the multiplexer (which selects data from different sources). Each unit is a logic gate that performs a basic boolean function (COPY, AND, OR, XOR).
• Labels for cross-referencing: The labels are used to cross-reference with the supplementary code and proofs. Each label indicates the module and the position of the logic gate within the module.

• Complete and accurate schematic: The figure provides a complete and accurate schematic of the four-bit computer, which is crucial for the reproducibility of the results and for verifying the claims made in the paper. The labeling allows for a precise mapping between the theoretical model and its implementation.
• Valid computer design: The design of the computer, as represented in the figure, is a valid implementation of a digital computer capable of simulating the target system.

• Detailed but complex diagram: The figure provides a detailed, labeled diagram of the four-bit computer. The use of labels for each unit (e.g., P₁, P₂, R₁, R₂, Co, X₁, A₁, etc.) is helpful for referencing specific components in the supplementary materials. However, like previous figures showing the computer, the sheer complexity of the diagram can be overwhelming for a reader. It is difficult to follow the connections and understand the overall flow of information without a very close examination.
• Clear caption: The caption is clear and concise, indicating that the units are labeled.
• Not referenced in the main text: The figure is not referenced in the main text, relegating it to supplementary material. While this is understandable given its complexity, it might be beneficial to reference it at least once in the main text to guide readers to this detailed schematic.

• Initial State of the Computer: Figure 13 depicts the four-bit computer (previously shown in Figures 2 and 12) at the very beginning of a simulation, a stage called 'Update 0: Initialization.' This is the starting point, where the computer is set up to mimic the initial state and transition rules of the target system, PQRS. The figure shows the state of every single logic gate (all 117 of them) within the computer. The black units are 'ON' (representing a binary value of 1), and the white units are 'OFF' (representing a binary value of 0). Specific parts of the computer are initialized: the data registers (which hold the current state of the simulated system) are set to match the initial state of PQRS (0101), and the program memory is loaded with the transition rules of PQRS. The clock is also set to its initial state.

• Crucial for accurate simulation: The initialization process is crucial for ensuring that the computer accurately simulates the target system. Setting the data registers to the initial state of PQRS and loading the program memory with the correct transition rules are necessary steps for a valid simulation.
• Complete and verifiable description: The figure, in conjunction with the supplementary text, provides a complete and verifiable description of the initialization process, allowing for replication of the simulation.

• Clear visual representation of the initial state, but inherently complex: The figure shows the four-bit computer in its initial state, ready to begin simulating the PQRS system. The use of color-coding (black for ON/1, white for OFF/0) is consistent and helps to visually represent the state of each unit. However, the figure is inherently complex, and understanding the initialization process requires careful attention to the details and the accompanying supplementary text.
• Clear caption: The caption is concise and clearly indicates the figure's purpose.

Figure 14: Update 1: The instruction register loads P's truth table, and current state selects a multiplexer input.

• Fetching Information for P's Next State: Figure 14 shows the four-bit computer during the first step ('Update 1') of simulating a single transition of the PQRS system. At this stage, the computer begins to determine what the next state of unit P in the PQRS system would be, given its current state. It does this in two main steps, as indicated in the caption. First, the 'instruction register' loads P's 'truth table.' The truth table, loaded into the program in the initialization, contains the information about how P should behave based on all possible inputs. Think of it like looking up the rules for P in a rulebook. Second, the current state of the PQRS system (stored in the data registers) 'selects a multiplexer input.' The multiplexer acts like a selector switch. Based on the current state of PQRS (0101), a specific input to the multiplexer is chosen. This selected input corresponds to the relevant part of P's truth table for the current situation.

• Valid implementation of simulation: The depicted process of loading the truth table information and selecting a multiplexer input based on the current state is a valid and standard way to implement a computational simulation of a system with defined state transitions.
• Verifiable simulation process: The figure, together with the supplementary text describing the computer's operation, provides a verifiable account of the simulation process at this specific update step.

• Clear visual representation, but requires background knowledge: The figure depicts the state of the four-bit computer at 'Update 1' of the simulation, focusing on the process of fetching information needed to compute the next state of unit P. The use of color-coding (black/white for ON/OFF) is consistent and helps visualize the state. However, understanding the specific operations and their sequence requires a good understanding of the computer's architecture and the accompanying supplementary text. The caption could be improved by explicitly mentioning that this update is part of the simulation of PQRS.
• Caption conciseness: The caption is informative, but very concise.

• Computation of P's Next State: Figure 15 shows the four-bit computer during the second step ('Update 2') of simulating a single transition of the PQRS system. At this point, the computer computes what the next state of unit P will be. The previous step (Figure 14) involved fetching the relevant information (P's truth table and the current state of PQRS). Now, that information is used. Specifically, the multiplexer, acting like a selector switch, uses the current state of PQRS (0101) to choose the correct output from the program memory. This output represents what P should do according to its transition rules, given the current state. The instruction register now loads Q's truth table, preparing for the next step.
• P's next state: The figure shows, by the states of the logic gates, that the next state of P will be 1 (ON).

• Valid computational procedure: The depicted process of using the current state and the truth table information to compute the next state of a unit is a valid and standard computational procedure.
• Verifiable computation process: The figure, combined with the supplementary text, provides a verifiable account of the computation performed at this update step.

• Clear visual representation, but relies on prior knowledge: The figure depicts the state of the four-bit computer at 'Update 2' of the simulation, specifically showing the computation of the next state of unit P. The consistent use of color-coding (black/white for ON/OFF) aids in visualizing the state. However, understanding the process requires familiarity with the computer's architecture and the sequence of operations. The caption could benefit by explicitly mentioning the ongoing simulation of the PQRS system.
• Concise caption: The caption concisely states the key operation occurring at this update step.

• Computation of Q's Next State and Propagation of P's next state: Figure 16 shows the four-bit computer during the third step ('Update 3') of simulating a single transition of the PQRS system. At this stage, the computer computes the next state of unit Q, mirroring the process used for unit P in the previous step (Figure 15). The output of the multiplexer (MO), which represents the next state of P (which was calculated in the previous step), is now propagated one step forward in the circuit. The computer is now using the current state of PQRS and the pre-loaded truth table information to determine what the next state of Q should be, based on the rules of the PQRS system. The instruction register now loads R's truth table.

• Valid computational procedure: The depicted process—computing the next state of a unit based on the current state and pre-loaded truth table information—is a valid and standard computational procedure for simulating system dynamics.
• Verifiable computation process: The figure, in conjunction with the supplementary text, provides a verifiable account of the computation performed at this update step.

• Clear visual representation, but relies on prior knowledge: The figure depicts the state of the four-bit computer at 'Update 3' of the simulation, specifically showing the computation of the next state of unit Q. The consistent use of color-coding (black/white for ON/OFF) aids in visualizing the state. However, understanding the process requires familiarity with the computer's architecture and the sequence of operations, as well as the previous steps. The caption could benefit by explicitly mentioning the ongoing simulation of the PQRS system.
• Concise caption: The caption concisely indicates the operation at this step.

• Computation of R's Next State and Propagation of P and Q's next states: Figure 17 shows the four-bit computer during the fourth step ('Update 4') of simulating a single transition of the PQRS system. At this stage, the computer computes the next state of unit R, following the same process used for units P and Q in the previous steps. The next state of P, which was computed in step 2 and propagated forward in step 3, is now represented by the state of a buffer unit (B3). The next state of Q is represented by the output of the multiplexer (MO). The computer is now using the current state of PQRS and the pre-loaded truth table information to determine what the next state of R should be. The instruction register now loads S's truth table.

• Valid computational procedure: The depicted process—computing the next state of a unit based on the current state and pre-loaded truth table information, and propagating previous results—is a valid and standard computational procedure for simulating system dynamics.
• Verifiable computation process: The figure, combined with the supplementary text, provides a verifiable account of the computation performed at this update step.

• Clear visual representation, but relies on prior knowledge: The figure shows the four-bit computer at 'Update 4' of the simulation, focusing on the computation of the next state of unit R. The color-coding (black/white for ON/OFF) consistently represents the state of each unit. However, understanding the specific operations and their sequence necessitates familiarity with the computer's architecture, as well as the previous steps in the simulation. The caption could be improved by explicitly mentioning the ongoing simulation of the PQRS system.
• Concise caption: The caption concisely describes the main action occurring at this update step.

• Computation of S's next state and propagation of prior results: Figure 18 shows the four-bit computer during the fifth step ('Update 5') of simulating a single transition of the PQRS system. At this stage, the computer computes the next state of unit S. The next states of P, Q, and R, which were computed in earlier steps, are now propagating through the buffer units (B1, B2, and B3). The computer is now using the current state of PQRS and the truth table to calculate the next state of S.

• Valid computational procedure: The process shown—computing the next state of a unit based on current state and truth table information—is a standard and valid computational procedure.
• Verifiable computation process: The figure, along with the supplementary text, gives a verifiable account of the calculations performed at this step.

• Clear visual representation, but requires prior knowledge: The figure shows the four-bit computer at 'Update 5' of the simulation, focusing on the computation of the next state of unit S. The color-coding (black/white for ON/OFF) consistently represents the state. However, to fully grasp the operations and their sequence, prior knowledge of the computer's architecture and the preceding simulation steps is required. The caption would be more informative if it explicitly stated that this update is part of the ongoing PQRS simulation.
• Concise caption: The caption concisely describes the main action taking place at this update step.

Figure 19: Update 6: Each simulated unit's next state arrives at its respective data register.

• Arrival of Next States at Data Registers: Figure 19 shows the four-bit computer during the sixth step ('Update 6') of simulating a single transition of the PQRS system. At this stage, the next states of all four units of the PQRS system (P, Q, R, and S) —which were computed in the previous steps—have propagated through the circuit and are now present at the inputs of their respective data registers. Specifically, these next states are present at the inputs of each data register's RXOR unit (i.e., B₁ to RXOR, B₂ to RXOR, B₃ to RXOR, and MO to RXOR).

• Necessary step in the simulation: The depicted process—the arrival of the computed next states at the data registers—is a necessary and valid step in the simulation process. It sets the stage for updating the stored state of the simulated system.
• Verifiable state of the computer: The figure, along with the supplementary text, provides a verifiable account of the state of the computer at this update step.

• Clear visual representation, but requires prior knowledge: The figure depicts the four-bit computer at 'Update 6' of the simulation. The color-coding (black/white for ON/OFF) consistently represents the state of each unit. However, understanding the illustrated process requires familiarity with the computer's architecture and the previous simulation steps. The caption would be more informative if it explicitly stated that this update is a step within the PQRS system simulation.
• Concise caption: The caption concisely describes the key event occurring at this update step.

• Clock Enabling Registers and XOR Comparison: Figure 20 shows the four-bit computer during the seventh step ('Update 7') of simulating a single transition of the PQRS system. At this stage, a specific part of the clock circuit (unit A₂) turns ON. This signal 'enables' each of the data registers. Enabling a register means preparing it to update its stored value based on the new inputs it has received. Each register's lower XOR unit receives two inputs: one from its upper XOR, which holds the current state of the simulated unit (P, Q, R, or S), and one from another unit that holds the computed next state of that unit. Each XOR gate performs a comparison of these two inputs, to determine if the register needs to change its state or not.

• Fundamental operation in digital circuits: The depicted process—using a clock signal to enable registers and prepare them for updating—is a fundamental and valid operation in digital circuits and computer architecture.
• Verifiable computer state: The figure, along with the supplementary text, provides a verifiable account of the computer's state at this update step.

• Clear visual representation, but relies on prior knowledge: The figure depicts the four-bit computer at 'Update 7' of the simulation, focusing on the clock signal enabling the data registers. The color-coding (black/white for ON/OFF) consistently represents the state. However, understanding the process requires familiarity with the computer's architecture and prior simulation steps. The caption would be more informative if it explicitly mentioned the ongoing simulation of the PQRS system and the purpose of enabling the registers.
• Concise caption: The caption concisely describes the key action at this update step.

• Propagation of Toggle Signals: Figure 21 shows the four-bit computer during the eighth step ('Update 8') of simulating a single transition of the PQRS system. During the previous step (Figure 20), the clock signal enabled each of the data registers, preparing them to update their stored values. Now, at Update 8, each register's 'toggle signal' is allowed to influence its stored value. The 'toggle signal' is the output of the AND gate within each register (RAND, RAND, RAND, RAND). This signal indicates whether the register's stored value needs to change to reflect the newly computed next state of the corresponding PQRS unit (P, Q, R, or S). If the toggle signal is ON (1), it means the current state and the next state are different, and the stored value should be flipped. If the toggle signal is OFF (0), it means the current state and the next state are the same, and the stored value should remain unchanged.

• Necessary step in the simulation: The depicted process—allowing the 'toggle signal' to influence the stored value in the registers—is a necessary and valid step in implementing the simulation. It ensures that the registers update correctly based on the computed next states.
• Verifiable computer state and operation: The figure, along with the supplementary text, provides a verifiable account of the computer's state and operation at this update step.

• Clear visual representation, but requires prior knowledge: The figure shows the four-bit computer at 'Update 8' of the simulation. The color-coding (black/white for ON/OFF) consistently represents the states of each unit. However, fully understanding the illustrated process and its significance requires familiarity with the computer's architecture and the preceding steps in the simulation. The caption accurately describes what happens in this step, but could mention that this step is part of the PQRS simulation.
• Concise caption: The caption concisely describes the key action taking place at this update step.

Figure 22: Update 9: The registers adopt the next state of PQRS, and the cycle repeats.

• Registers Update to the Next State of PQRS: Figure 22 depicts the four-bit computer during the ninth step ('Update 9') of simulating a single transition of the PQRS system. This is the final step of a single simulation iteration. At this point, the data registers, which store the current state of the simulated PQRS system, update their values to reflect the newly computed next state. The units RSIM, RSIM, RSIM, and RSIM simultaneously adopt the values that were determined by the previous computations. After this update, the computer is ready to begin the next cycle, simulating the next state transition of PQRS, starting again from 'Update 1'. This completes one full cycle of the simulation.
• Specific state change: The figure shows the states of RSIM, RSIM, RSIM, and RSIM changing to 1110. This corresponds to the next state of PQRS, given the example initial state of 0101.

• Crucial final step in simulation: The updating of the registers with the newly computed next state is the final, crucial step in correctly simulating the dynamics of the PQRS system. This ensures that the computer's internal representation of PQRS is updated according to the defined transition rules.
• Verifiable account of the simulation cycle: The figure, together with the supplementary text, provides a verifiable account of the computer's state and operation at this update step, completing the description of a full simulation cycle.

• Clear visual representation, but relies on prior knowledge: The figure shows the four-bit computer at 'Update 9' of the simulation, which completes one full cycle of simulating a single state transition of the PQRS system. The color-coding (black/white for ON/OFF) is consistent, allowing for visual tracking of the state changes. However, understanding this final step requires familiarity with all the preceding steps and the overall architecture of the computer. The caption clearly states the two key events: the update of the registers and the beginning of a new cycle.
• Indication of cyclical process: The figure and caption indicate that the simulation process is cyclical and can continue indefinitely.

• System Composition and Dynamics: Figure 1 presents a system named PQRS, designed for simulation. This system is made up of four interconnected units, and each of these units can be in one of two states, represented as binary values (0 or 1). Think of each unit like a light switch that can be either OFF (0) or ON (1). The way these units interact and change their states over time is defined by a truth table, or more generally, a transition probability matrix. A truth table is a simple way to show all possible combinations of inputs (the states of the four units) and their corresponding outputs (the next states of the units). A transition probability matrix, on the other hand, is a table that contains the probabilities of transitioning from one state to another. This matrix is helpful when the change of state is not definite but probabilistic. The figure consists of multiple parts (A, B, C) to fully describe the system.

• Methodological approach: The introduction of the target system (PQRS) is methodologically sound. The use of binary units and representation via a truth table/transition probability matrix are standard and valid approaches for modeling system dynamics in computational neuroscience and related fields.
• Foundation for simulation: The figure provides a clear foundation for subsequent simulations. It establishes the basic parameters and rules governing the system, which is critical for the reproducibility and validity of the simulation results.

• Integration of figure panels: The figure effectively introduces the target system (PQRS) and its components, providing a clear visual representation and explanation of its dynamics. However, splitting the figure into multiple panels (1A, 1B, 1C) makes it slightly harder to follow as a single cohesive unit. Combining these or better integrating the information could improve the flow.
• Clarity of system dynamics: The use of a truth table and transition probability matrix is well-explained and appropriate for the intended audience, enhancing the overall clarity of how the system's dynamics are defined.

• Overall System and Components: Figure 2 depicts a digital computer, built with digital logic gates, specifically designed to simulate the behavior of the PQRS system described earlier. The computer operates using a four-bit system. In digital systems, "bit" refers to the smallest unit of data, representing a single binary value (0 or 1). A four-bit computer, therefore, processes information in chunks of four binary digits. The figure visually represents how the computer achieves this simulation. The computer contains 117 units. Each unit is a logic gate, which performs a basic boolean function (COPY, AND, OR or XOR). A boolean function takes one or more binary inputs and returns one binary output. The circuit includes components like a clock (which synchronizes operations), frequency dividers (which create slower clock signals from a faster one), program memory (where instructions are stored), data registers (which store the state of the PQRS system), and a multiplexer (which selects data from different sources). These components work together to mimic the state transitions of the PQRS system.
• Indefinite Simulation Capability: The computer is said to be capable of simulating PQRS "indefinitely." This implies that the computer can continuously run the simulation of the PQRS system without any inherent limit, repeatedly cycling through its states as defined by its transition rules.

• Validity of simulation approach: The concept of simulating a system with defined dynamics using a digital computer is scientifically sound. The design of the computer, as presented, is a valid approach to implementing such a simulation, utilizing standard digital logic components.
• Supports the functional simulation claim.: The figure provides the structural basis for the claim that a computer can functionally simulate the PQRS system. This is a crucial step in their argument that functional equivalence does not necessitate phenomenal equivalence.

• Complexity of the visual representation: The figure introduces a four-bit computer designed to simulate the PQRS system. The visual representation is complex, and while it shows the components, the sheer number of connections and units might be overwhelming for a reader unfamiliar with digital circuit diagrams. A simplified, high-level overview diagram might be beneficial before presenting the complete circuit.
• Caption and reference text clarity: The caption clearly states the figure's purpose. The reference text is concise.

Figure 3: Identifying the computer's complexes and unfolding their cause-effect structures.

• Overall Analysis and Result (φs = 0 ibits): Figure 3 presents the results of analyzing the four-bit computer, described in Figure 2, using a framework called Integrated Information Theory (IIT). IIT provides tools to determine if a system is conscious, and to what degree. Key to this is the concept of "system integrated information" (represented by the symbol φs, or "phi_s"). It represents the extent to which the system's internal interactions (its "cause-effect power") is affected if the system is split into independent parts. The figure shows that when the computer, as a whole, is analyzed, its φs value is 0 'intrinsic bits' (ibits). "Intrinsic bits", or ibits, are the unit of measurement of system integrated information. The reference text specifically points to panel A (highlighted in grey) as showing this result. A value of 0 means the computer, as a whole, is not integrated and has no cause-effect power above and beyond its individual parts. The figure shows the computer breaking down ("fragmenting") into 24 smaller 'complexes' (shown in blue in Fig 3A). A 'complex,' in IIT, is a set of elements that is integrated, i.e. has intrinsic cause-effect power. Each of these small complexes is made up of only a few units.

• Methodological validity: Applying IIT's causal power analysis is a methodologically valid approach within the context of the paper's theoretical framework. The result (φs = 0 ibits) is a key finding, indicating that the computer, despite simulating the PQRS system, does not possess integrated information at the system level.
• Consistency with IIT principles: The finding that the computer fragments into multiple small complexes is consistent with the principles of IIT. The lack of integration at the global level is a direct consequence of the computer's architecture, as highlighted in the paper.

• Clarity and accessibility of the figure: The figure aims to demonstrate the results of applying Integrated Information Theory's (IIT) causal power analysis to the computer. The reference to Fig. 3A (grey) is clear, indicating where to look for the specific result (4s = 0 ibits). However, the figure itself is very complex, and it may be difficult for readers to understand the significance of the different colored components and the meaning of fragmentation into multiple complexes without significant prior knowledge of IIT.
• Caption could provide more context.: The caption is descriptive, but could be more informative. It introduces the concepts of 'complexes' and 'cause-effect structures' without defining them, which could hinder understanding for readers unfamiliar with IIT.

Figure 4: Identifying a system's intrinsic units based on maximally irreducible cause-effect power.

• Explanation of Intrinsic Units and Maximally Irreducible Cause-Effect Power: Figure 4 explains how Integrated Information Theory (IIT) determines what constitutes the fundamental building blocks ('intrinsic units') of a system that can support consciousness. IIT asserts that consciousness depends on a system's ability to exert influence over itself ('cause-effect power'). Furthermore, the way in which the system exerts influence is crucial. 'Intrinsic units' are those components that maximize this cause-effect power in an irreducible way. "Irreducible" means that the cause-effect power of the whole is greater than the sum of the cause-effect power of its parts. The figure describes a process, in principle, of finding these intrinsic units. This process involves considering the system at different levels of granularity or "grains." At the finest level are the 'micro units' (the smallest components). We can then group these micro units into larger units called 'macro units'. The process involves testing all possible combinations of groupings to see which grouping maximizes the system's cause-effect power. Figure 4A is referenced as illustrating this concept.
• Concept of 'Grains' (Micro and Macro): The reference text mentions evaluating "all possible grains". A "grain" refers to the level of detail considered in the system. A "micro" grain is the finest possible level. A "macro" grain combines multiple micro-level components. The point is that the "intrinsic units" might actually be combinations of smaller units, if those combinations have greater cause-effect power than the individual components.

• Methodological validity within IIT: The concept of identifying intrinsic units based on maximizing integrated information is a core tenet of IIT. The described process of exhaustively evaluating different groupings of units is, in principle, a valid method for determining these intrinsic units, although computationally challenging.
• Accurate representation of IIT's framework: The figure and its accompanying text accurately represent the theoretical framework of IIT regarding the determination of intrinsic units.

• Heavy reliance on IIT-specific terminology: The figure explains a core concept of IIT: how to identify a system's 'intrinsic units.' The caption is descriptive, but relies heavily on technical jargon ('maximally irreducible cause-effect power') that is not immediately accessible to a general audience. The reference text introduces more jargon ('complex,' 'intrinsic units,' 'grains,' 'micro units,' 'macro units') which may be confusing. The figure itself (specifically panel A, as referenced) uses abstract representations (shapes and arrows) that, without a deeper understanding of IIT, are difficult to interpret.
• Connection between text and visuals could be stronger: While panel A is referenced, the connection between the textual description and the visual representation in panel A could be made more explicit. The text mentions 'exhaustively grouping subsets,' but the visual depiction of this process is abstract.
• Complexity of the process not fully conveyed visually: The reference to multiple subfigures ([34, 38, 39, 44]) suggests a complex process, but the figure itself doesn't fully convey the iterative and exhaustive nature of the evaluation.

Figure 5: The computer does not replicate the target's cause-effect structure at any macro grain.

• Explanation of 'Macroing' and the Specific Groupings Used: Figure 5 illustrates an attempt to analyze the four-bit computer (from Figure 2) at a coarser level of detail, called the 'macro grain.' Instead of looking at individual logic gates (the 'micro' level), the figure groups these gates into larger functional blocks. For example, each line of the computer's program memory, along with its associated unit in the instruction register, is considered as a single macro unit (labeled α through π). The state of each of these macro units is then defined by the state of its instruction register unit, simplifying the overall analysis. The idea is to see if, at this higher level of abstraction, the computer does replicate the cause-effect structure of the target system (PQRS). The caption states that it does not, even with this simplification.
• Emphasis on a Single Example of Macroing: The figure highlights one specific way of grouping the computer's components. The reference text clarifies that this is just one example of how the computer could be analyzed at a macro level, implying there are other possible groupings. The figure shows that even with this grouping designed to mimic the function, the system is not integrated (φs = 0 ibits)

• Validity of the macro grain analysis approach: The approach of analyzing the system at a macro grain is consistent with the principles of IIT, as discussed in relation to Figure 4. The specific macroing presented is a reasonable attempt to align the computer's components with functional roles, reflecting a computational perspective.
• Support for the claim of non-replication: The figure's claim, that this macroing does not replicate the target's cause-effect structure, is supported by the analysis presented in the paper. The specific groupings and the resulting lack of integration (φs = 0 ibits) highlight the core argument that functional equivalence does not guarantee phenomenal equivalence.

• Complexity of the visual representation and lack of clear demonstration: The figure presents a specific 'macroing' of the computer, grouping micro-units into larger functional units. The visual representation is complex, making it difficult to immediately grasp the proposed groupings and their implications. The caption states the conclusion, but the figure itself doesn't clearly demonstrate why this particular macroing fails to replicate the target's cause-effect structure.
• Use of jargon: The reference text uses terms like 'extrinsic, computational-functionalist perspective' which, while technically precise, may not be readily understood by all readers. More accessible language could improve communication.

• Illustration of Dissociation Concept: Figure 6 illustrates a core argument of the paper: that a system's function (what it does) can be completely different from its cause-effect structure (what it is, according to IIT). It presents a visual comparison of the cause-effect structures of two different systems: the original target system, pQrS, and the four-bit computer designed to simulate it and a third system WXYZ. The cause-effect structure, in IIT, represents the way a system's components constrain each other's past and future states. The figure shows that even though the computer can perfectly mimic the input-output behavior (the function) of pQrS (and WXYZ), their underlying cause-effect structures are vastly different. The cause-effect structures are represented by geometrical shapes.
• Description of the structures: The top left shows the complex and rich cause-effect structure of pQrS (Φ = 391.25 ibits). The top right shows the cause-effect structure of WXYZ, which implements rule 110 (Φ = 2.8 ibits and Φ = 0.6 ibits). The bottom shows that the computer, whether simulating pQrS or WXYZ has a fragmented structure. The structures are nearly identical. The label 'CES' refers to 'Cause-Effect Structure'.

• Accurate representation of IIT analysis results: The figure accurately depicts the results of applying IIT's analysis to both the target system and the simulating computer. The visual representation of the cause-effect structures, while complex, is consistent with the theoretical framework. The claim of dissociation is directly supported by the contrasting structures.
• Strengthening of argument: The introduction of WXYZ and showing that the computer fragments in the same way when simulating it is a good addition, strengthening the dissociation argument.

• Effective visual contrast and clear caption: The figure visually contrasts the cause-effect structures of the target system (pQrS) and the computer simulating it, as well as another system (WXYZ). The use of different colors and the clear separation of the structures highlight the differences effectively. The caption directly states the key takeaway: a dissociation between function and cause-effect structure.
• Use of undefined abbreviations.: The figure uses abbreviations like 'CES' which are not defined in the caption or the provided reference text, potentially hindering comprehension for readers who have not read the whole paper closely. Although the figure shows different systems, it does not give an intuitive explanation of the differences.

• Dynamic Evolution of Cause-Effect Structure: Figure 9 illustrates how the cause-effect structure of the PQRS system changes as it transitions through its various possible states. Each panel in the figure represents a specific state of the PQRS system (e.g., 'pqrs', 'Pqrs', etc., where lowercase represents 0 and uppercase represents 1 for each of the four units). Within each panel, the cause-effect structure, as defined by Integrated Information Theory (IIT), is depicted. This structure shows how the system's components constrain each other's past and future states. The arrows between the panels show how the system transitions from one state to another. The system can exist in any of five different "cycles". A cycle is a repeating sequence of states. The figure shows that the system's cause-effect structure changes depending on its current state. The table shows, for each state, the integrated information of the system and of the complexes, the number of distinctions and relations and a description of the distinctions.
• Complete State Space Representation: The figure shows all 16 possible states of the four-unit PQRS system. The transitions between the states are deterministic, meaning that the next state is completely determined by the current state.

• Complete and accurate representation of system dynamics: The figure provides a complete and accurate representation of the dynamics of the PQRS system, as defined by its transition rules. This is crucial for supporting the paper's claims about the dissociation between function and cause-effect structure, as it allows for a direct comparison between the computer's simulation and the target system's inherent dynamics.
• Consistency with IIT principles: The unfolding of the cause-effect structures for each state is consistent with the principles of IIT. The figure serves as a valuable reference for understanding how the system's internal structure changes over time.

• Comprehensive but visually dense presentation: The figure presents a comprehensive overview of the cause-effect structures of the PQRS system across all its possible states. The use of multiple panels, each representing a different state, is effective in showing the dynamic evolution of the system. However, the complexity of the individual cause-effect structures, combined with the sheer number of states presented, makes the figure visually dense and potentially overwhelming. The use of arrows to show transitions is clear, but a more concise summary or a way to navigate the different states interactively might improve comprehension.
• Caption could be more explicit: The caption is concise but could benefit from explicitly mentioning that the figure shows the dynamic evolution of the cause-effect structure.
• Summary table could be improved.: The table summarizing the complexes, distinctions, relations and integrated information is useful, although it could be better integrated with the visual representations. The use of abbreviations within the table is not defined.

Table 1: The state of each timekeeping unit over the course of the first 16 updates

• Clock Components and their States Over Time: Table 1 shows how the 'clock' components of the four-bit computer change their state over the first 16 steps (updates) of the simulation. The clock is crucial for synchronizing the operations of the computer. The table has rows representing the different time steps (from Update 0 to Update 15) and columns representing the different components of the clock: Co, X1, A1, X2, and A2. Each cell in the table contains either a '0' or a '1', representing the binary state (OFF or ON) of that specific clock component at that specific time step. For example, at Update 0, Co is ON (1), while all other components are OFF (0). The sequence of 0s and 1s shows how the clock components oscillate and generate the timing signals needed for the computer's operation.
• Clock component roles: Co is the core oscillator, and X1, A1, X2, A2 are frequency dividers. The table clearly shows how the frequency dividers create slower clock signals. For example, X1 changes state every two updates, A1 every four updates, X2 every eight updates and A2 is ON on update 8 and 15.

• Accurate representation of clock behavior: The table accurately represents the behavior of the clock and frequency divider circuit described in the supplementary material. The states of each unit (Co, X1, A1, X2, A2) follow the correct logic based on their connections and functions (COPY, AND, and NOT).
• Essential for understanding simulation timing: The information presented in the table is essential for understanding the timing of the simulation and verifying the correct operation of the computer.

• Clear and concise presentation: The table clearly and concisely presents the state of each timekeeping unit (Co, X1, A1, X2, A2) over the first 16 updates of the simulation. The use of 0s and 1s is standard for representing binary states. The table format is well-organized and easy to read.
• Accurate caption: The caption accurately describes the table's contents.

Table 2: Potential relations involving Sn for an imperfect ring of at least five units.

• Explanation of Potential Relations and their Components: Table 2, in the context of Integrated Information Theory (IIT), explores how a specific unit, labeled 'Sn', interacts with other units within a particular structure called an 'imperfect ring'. An imperfect ring is like a chain of connected units where most units only affect their immediate neighbor, but with a specific modification involving Sn. The table lists all possible 'relations' that involve Sn. In IIT, a 'relation' describes how different parts of a system constrain each other's past and future states. Each row in the table describes one such potential relation. The "d" column describes which elements are involved in this relation. The "faces" column describes which parts of the cause-effect structure are involved (e.g. are the elements constraining past states, future states or both). The "overlap" column shows which element is shared between the involved distinctions. The 'max φr' column presents the maximum possible value of 'integrated information' (φr) for each relation. Integrated information, in this context, quantifies how much a system is interconnected and irreducible to its parts. The values in the 'max φr' column represent the upper limit of how much each relation could contribute to the overall integrated information of the system.

• Consistent with IIT's mathematical framework: The table is derived from the mathematical framework of IIT and accurately represents the potential relations that can exist within the specified 'imperfect ring' structure. The listed relations and their corresponding 'max φr' values are consistent with the theory's postulates and calculations.
• Contributes to the overall argument: The table contributes to the overall argument by providing a detailed breakdown of the potential contributions to integrated information within a specific type of system, supporting the claim about the limitations of computers in replicating cause-effect structures.

• Clear organization, but relies heavily on IIT jargon: The table lists potential relations involving the unit Sn in an imperfect ring structure within the context of Integrated Information Theory (IIT). The organization of the table is clear, with columns for the distinctions involved, the types of faces (cause-effect, cause-cause, etc.), the overlap between purviews, and the maximum value of φr (integrated information for a relation). However, understanding the table requires significant familiarity with IIT concepts and terminology. The use of abbreviations (like 'd(s1)') without explicit definitions within the table caption hinders accessibility.
• Caption could provide more context: The caption is concise but could be more informative by explicitly mentioning that these relations are relevant to calculating the overall integrated information (Φ) of the system.

Figure 7: Inductive extension to large computers simulating arbitrarily complex systems.

• Extension of the Dissociation Argument to Larger Systems: Figure 7 extends the core argument of the paper—the dissociation between function and cause-effect structure—to larger and more complex systems. It does this by showing, visually, how the four-bit computer can be scaled up to simulate systems of arbitrary size and complexity. It shows an "arbitrarily large, finite computer" simulating a "Rule 110 cellular automaton", which is known to be Turing-complete. A Turing-complete system is one that can, in principle, perform any computation that any other computer can. This implies that the limitations identified in the four-bit computer regarding cause-effect structure are not specific to its small size, but are inherent to its architecture and, by extension, to similar computer architectures.
• Difference in Φ.: Panel B indicates that the difference in integrated information (Φ) between the target systems and computer micro-complexes will grow as the systems become larger. The target system's Φ can grow at a rate of O(2^(2^n)) where n is the number of units. The computer's Φ on the other hand grows at O(3n/2). O() refers to the order of growth.

• Logical soundness of the inductive extension: The inductive extension to larger systems is logically sound. Given the demonstrated limitations of the four-bit computer's architecture, it's reasonable to extrapolate that similar limitations would hold for larger computers built on the same principles. The reference to Turing completeness via Rule 110 cellular automata correctly implies the generality of the argument.
• Consistency with IIT principles: The claim that the dissociation can be 'exacerbated' if the targets are large and have high Φ is consistent with the theoretical framework of IIT. Systems with higher Φ have richer cause-effect structures, which are even less likely to be replicated by the fragmented architecture of a standard computer.

• Effective use of visuals and concise caption: The figure illustrates how the principles demonstrated with the four-bit computer can be extended to larger and more complex systems. The use of visual representations of a larger computer, a Rule 110 cellular automaton, and a Turing machine effectively conveys the concept of scalability. The caption is clear and concisely describes the figure's purpose.
• Conceptual illustration rather than rigorous demonstration: While the figure shows the possibility of extension, it doesn't provide concrete details about how the analysis would be performed on these larger systems. This makes it more of a conceptual illustration than a rigorous demonstration.

• Conceptual Model of Double Dissociation: Figure 8 presents a conceptual model arguing that intelligence and consciousness are not necessarily linked and can exist independently of each other. This is depicted as a 'double dissociation,' meaning that you can have high intelligence with low consciousness, and vice-versa. The figure uses a simple two-by-two diagram. One axis represents the level of 'Intelligence,' ranging from low to high. The other axis represents the level of 'Consciousness,' also ranging from low to high. Different entities are placed within this space to illustrate the concept. For example, 'biological systems' are placed in the high-intelligence/high-consciousness quadrant, while a hypothetical 'artificial intelligence without consciousness' is placed in the high-intelligence/low-consciousness quadrant.
• Examples in each quadrant: The diagram includes examples to illustrate each quadrant: biological systems (high intelligence, high consciousness), hypothetical AI (high intelligence, low consciousness), and cerebral organoids (low intelligence, potentially high consciousness). It also includes a point with low intelligence and low consciousness.

• Theoretical validity of the double dissociation: The concept of a double dissociation between consciousness and intelligence is a valid theoretical proposition, supported by the arguments and analysis presented in the paper. The figure serves as a visual aid to this concept, illustrating the possibility of systems that are intelligent but not conscious, and vice versa.
• Speculative but illustrative examples: The placement of specific examples within the grid (e.g., AI, cerebral organoids) is speculative, but consistent with the paper's overall arguments and serves to illustrate the theoretical possibilities.

• Effective use of a conceptual diagram: The figure presents a conceptual diagram illustrating the potential for a double dissociation between consciousness and intelligence. The use of a two-by-two grid with labeled axes (Consciousness and Intelligence) is a clear and effective way to represent this concept. The placement of different entities (biological systems, AI, etc.) within the grid visually conveys the core idea.
• Clear caption: The caption clearly states the main point of the figure. The reference text provides context, although it is not directly related to the figure content itself.