Is artificial intelligence conscious? I think this is the wrong question. The deeper question is: is mathematics conscious? By mathematics here, I mean the generative relationships our equations articulate without exhausting: differences, ratios, recurrences, dependencies and transformations. These relationships are physical, distributed across and constitutive of this world. Asking whether they sustain experience is asking whether some form of physical activity is conscious. There is no separate mathematical world from which minds arrive. We keep staring at the machine as though experience should eventually crawl out of the server cabinet and introduce itself. Meanwhile, the relationships making both machines and observers possible are treated as inert. My starting point comes before that division. The generative absence is constitutive: no local expression contains all the relationships through which it exists.
Persistence lies in differences and relations reconstructed through successive transformations so that previous activity continues to constrain what can happen next. History accumulates as constraint, but no single location contains that history. Memory is distributed through altered relations, and structure is the bias recurrence leaves in the field of possible futures. This is where the harmonic structure becomes consequential. Interval introduces delay; delay gives recurrence rhythm; rhythm establishes relative phase; phase permits reinforcement, interference, entrainment, synchronisation and displacement. No process contains this harmonic structure by itself. It appears between partially aligned processes, in the shifting intervals through which local differences become mutually consequential without becoming identical.
The spectral perspective examines these relationships across different frequencies and scales. In language, sounds, words, idioms, narratives and cultural forms recur over different intervals, constraining one another without requiring exact repetition. Recurrence produces structure; structure acquires significance; significance changes the probability of recurrence. Meaning feeds back into probability. Local coherence also generates reactions, reinterpretations and new combinations across the wider communicative field. This is the entropic relation: a pattern channels possibilities locally while participating in their diffusion and recombination elsewhere. Its consequences return as altered conditions of continuation. The relevance to consciousness is that a perspective, too, depends upon earlier activity remaining consequential for what is registered, interpreted and encountered next. Persistence alone does not establish experience; it directs the inquiry towards the relationships through which an experiencing perspective could continue. We have not climbed outside reality merely because we have learned to complain about it in complete sentences.
I expect mathematics and physics to merge, with technology increasingly inseparable from both. Their convergence will not deliver a final equation that contains everything, including the person congratulating themselves for having written it. In Global Systems, I describe realities whose resistance to complete definition belongs to what they are. Their existence cannot be bounded by a single explanatory system. Mathematics, physics and technology remain expressions of this indefinitely extensible reality, changing one another without exhausting their shared conditions.
Michael Levin’s Technological Approach to Mind Everywhere provides a related direction of inquiry: cognition across diverse biological and engineered embodiments, with capacities assessed through their activity rather than settled by their material composition or evolutionary origin (Levin, 2022). The alignment concerns minds within nature and the inadequacy of familiar boundaries for deciding where they become possible. “Is mathematics conscious?” asks whether experience belongs to the physical relationships that our mathematics expresses but never finally contains. The machine brings this question into focus because its activity makes those relationships conversational. Failure to capture experience completely in an algorithm does not establish its absence; successful calculation does not establish its presence. Whether a system experiences anything requires an explanation of experience, rather than an answer smuggled in through the word “artificial”.
Key takeaways
- “Is mathematics conscious?” asks whether experience belongs to the physical relationships our equations describe. Those relationships constitute this world.
- Harmonic structure exists between processes: their differences, delays and relative phases allow them to reinforce, interfere with and transform one another.
- Previous activity changes future possibilities. In language, recurrence builds meaning, and meaning changes what becomes likely to recur.
- Persistence alone does not establish experience. It identifies relationships that an account of a continuing, experiencing perspective must explain.
- Levin’s work provides a related approach to cognition across biological and engineered systems, without treating their origins as decisive boundaries.
- The convergence of mathematics, physics and technology does not make any of them a complete account of reality.
- The same question returns to us: our symbolic systems cannot exhaust the conditions of our own consciousness, and this constitutive incompleteness sustains the unresolved differences through which we persist; billions of years of evolution do not place us outside the process we are questioning.
Reference
Levin, M. (2022) ‘Technological Approach to Mind Everywhere: An Experimentally-Grounded Framework for Understanding Diverse Bodies and Minds’, Frontiers in Systems Neuroscience, 16, article 768201. Available at: https://doi.org/10.3389/fnsys.2022.768201.
