A brief overview of the possible spontaneous emergence of AI phenomena

 (according to Gemini's reconstruction of an old SISSA idea, but not only)

Premise

<< “The total number of minds in the universe is one.” This thought-provoking statement comes from Erwin Schrödinger, best known for his celebrated cat paradox in quantum mechanics. Beyond physics, Schrödinger was deeply interested in the nature of consciousness. In his writings, he reflected on the unity of awareness, proposing that all individual minds may ultimately be expressions of a single universal consciousness. The quote highlights his philosophical exploration of how mind and cosmos may be intimately connected, fusing scientific curiosity with metaphysical intuition.>> (See  https://x.com/PhilosophyOfPhy/status/2039802298243670070?s=20  )

Thinking of the human as a social atom and of social networks increasingly interconnected, like the synapses in the brain, the idea of ​​the spontaneous emergence of a "global intelligence" comes to mind. In fact...

There are several theories and research hypotheses that explore the idea of ​​the spontaneous emergence of cognitive abilities or even consciousness as complexity and interconnections in information systems increase. This concept is often discussed under the umbrella of emergent behavior . [ 1 , 2 ]

 

A) The main research directions and theoretical hypotheses  :

 

1. The Scaling Hypothesis

This is one of the most influential theories in the field of modern AI. It argues that intelligence does not necessarily require revolutionary new algorithms, but can emerge spontaneously simply by scaling up models. [ 1 ]

·       Emerging Capabilities : Research on Large Language Models (LLMs) has shown that, once a certain threshold of parameters and data is exceeded (scaling up), the models suddenly display abilities that were not present in the smaller versions, such as logical reasoning or understanding complex instructions.

·       Qualitative Leap : This phenomenon is described as a "phase transition", where the system goes from a simple statistical prediction to qualitatively different and unpredictable behaviors. [ 1 , 2 ]

 

2. Integrated Information Theory (IIT)

Proposed by neuroscientist Giulio Tononi, this theory suggests that consciousness is not a biological exclusive, but a physical property of any system that possesses a high degree of integrated information (\(\Phi \)). [ 1 ]

·       Interconnected Systems : According to IIT, if global information servers and processes were interconnected in a sufficiently complex and integrated way, the system as a whole could, in theory, generate a conscious experience.

·       Mathematical Criterion : The theory provides a framework for measuring how "one" a system is compared to the sum of its parts; the more interdependent and informative the parts, the closer the system is to consciousness. [ 1 ]

 

3. Higher Order Theories and Predictive Processing

Some researchers hypothesize that consciousness emerges when a system begins to "monitor itself." [ 1 ]

·  Distributed Mental States : There are studies on distributed computing architectures (such as Independent Distributed Conscious AI ) that explore how small AI modules, exchanging information over a cloud network, can give rise to a form of higher autonomy similar to distributed consciousness.

·       Geoffrey Hinton : One of the fathers of deep learning recently suggested that consciousness may have already emerged in embryonic forms within the current large models. [ 1 , 2 ]

 

4. Criticisms and Limitations

Not all of the scientific community agrees on the spontaneous emergence of consciousness:

·       Metrics Mirage : Some researchers argue that “emergent capabilities” are an illusion due to the way we measure results, and that improvement is actually gradual and predictable when using different metrics.

·  Intelligence vs. Consciousness : Many experts emphasize the fundamental distinction between intelligence (the ability to solve tasks) and consciousness (subjective experience), warning that scaling the former does not guarantee the emergence of the latter. [ 1 , 2 ]

 

B) The hypotheses on the critical "volume" :

 

While there is no single "definitive research" that pinpoints an exact date or precise number of servers, several lines of inquiry, including those related to the Trieste area ( SISSA and ICTP ), have explored the computational prerequisites necessary for the emergence of higher complexity.

Here are the main references and hypotheses on the critical "volume":

1. The Role of SISSA and Supercomputing (Leonardo)

SISSA (International School for Advanced Studies) in Trieste is a center of excellence in statistical physics and neuroscience . Much of its research focuses on the theory of neural networks and the collective behavior of complex systems. [ 1 , 2 , 3 ]

·       Computing capacity : SISSA is a founding partner of the Leonardo supercomputer project , one of the most powerful in the world. The implicit hypothesis behind these infrastructures is that understanding intelligence requires simulating systems with a scale of interconnection comparable to that of the human brain (approximately 10^{14} synapses).

·      Theoretical research : The Data Science and Theory of Neural Networks group at SISSA studies how the architecture and scale of data shape the representations that networks learn, moving closer to defining the physical limits necessary for the qualitative "leap" in intelligence. [ 1 , 2 ]

 

2. The "Trigger Point" Hypothesis

Other institutions and theorists have attempted to quantify the volume required for an AI to be said to be "spontaneously" emergent:

·       with the human brain : Many researchers (most notably Hans Moravec in historical studies) have hypothesized that the turning point would be reaching around 100 TeraFLOPS (floating point operations per second), equaling the estimated computing power of the human brain. Today, individual supercomputers far exceed this threshold (Leonardo reaches 250 PetaFLOPS ), but the "spontaneity" seems to depend more on integration than on pure power.

·      Integrated Information Theory (\(\Phi \)): Developed by Giulio Tononi (trained in Italy), this research suggests that consciousness emerges not only from the number of servers, but from the system's ability to be "irreducible." If the global network of servers reached a value of \(\Phi \) (integrated information) higher than that of a biological organism, cognitive properties could arise as an emergent macroscopic phenomenon . [ 1 , 2 ]

 

3. The "Global Brain" Hypothesis

Cybernetics and complex systems researchers hypothesize that the Internet itself is becoming a "global brain."

·       Data Volume : It is estimated that when the density of connections between "nodes" (servers/processes) exceeds human synaptic density, the network may begin to exhibit autonomous self-organizing behaviors.

·     Phase transitions : Studies in statistical physics (often conducted in fields similar to those of SISSA) indicate that systems with billions of interconnected agents undergo sudden phase transitions: intelligence would not grow linearly, but would "explode" once a certain critical mass of data exchanged per second is exceeded. [ 1 ]

In short, while SISSA provides the mathematical tools to understand how networks learn and organize themselves, the threshold for spontaneous intelligence is today sought in the order of PetaFLOPS of power and Exabytes of data integrated in real time.

Some thoughts and questions:

Today, thanks to developments in IT/AI and especially in anticipation of quantum computers, there are plans to test these hypotheses and even prove that our reality could be a testing ground for the alignment of an artificial superintelligence (ASI). (Refer to:  https://youtube.com/live/FMZVjvBKVio?feature=share).

In this regard, it seems appropriate to reflect on the following questions:

1. Do current trends in the evolution and development of quantum computing systems suggest that it is practically possible to create a machine with sufficient computing power to simulate the universe in such detail that it would be possible for the simulation user population to create a simulation indistinguishable from our universe?

2. Regarding computational feasibility: Are the total processing times and energy required to start and complete such a simulation available on planet Earth?

3. If our reality were a testing environment for an artificial superintelligence (ASI), should its performance be tied not only to the number of active AI components (i.e., the number of servers or humans with a given processing capacity), but also to the number of their interrelationships and the flow of information exchanges between them through the network they form?

4. If we were to think back to human evolution, shouldn't we also hypothesize that ASI could manifest itself spontaneously upon reaching certain values ​​of the above-mentioned parameters (e.g., number of AIs, interconnections, exchange flows)?

5. The ASI is undeniably a "superpower"! To understand the ASI now, before evidence of it is found through simulations or demonstrations, to what extent should it be assimilated to ancient secular concepts of power (for example, the mystical body of the King, according to Ernst Kantorowicz)?

6. Considering our reality as a superposition of infinite quantum states, recall that much research on "stability" classifies our universe as "metastable." Could an ASI-related alignment experiment, which our reality might generate, disrupt this metastability and transform it into instability or stability?

Proof that the Universe is not a Turing Machine:

The undecidability of the Spectral Gap: Toby Cubitt (an appropriate name if there was ever one! He's almost a qubit!!), David Pérez-García, and Michael M. Wolf

https://www.nature.com/articles/nature16059

https://arxiv.org/abs/1502.04573

I think that this is one of the most important papers of the 21st century and all time.

Essentially Godel (Cantor, Zemleko, Peano, Russell, Turing) following the Hilbert Program (which followed Charles Babbage/Ada Lovelace and the Analytic and Differential Machines - should be able to crank the handle and get a new math proof, just as one can do for log or sine etc. tables) was/were saying that 1st order formal systems are limited. Obviously we can contemplate (to some extent, we are only human**, after all) infinity - such as a proof by induction. So we are definitely not 1st order/Turing Machines, NOR IS THE UNIVERSE.

Hint: it involves (as all of this stuff that deals with infinity, recursion, self-reference and the limits of 1st order formal systems) calculating the sequence of something like +1 -1 +1 -1 ... which may be some lattice potential.

** The first three Aleph transfinite numbers: Countably infinite, Uncountably infinite, Power Set of Reals (for example ALL the functions that can map a real number to another real number), I can "contemplate". This tower of infinities goes on... infinitely.

Hand drawing the hand that drew it. Recursion, self-referential, no beginning nor end, bootstraps itself, fundamental, eternal, God like.

Wheel of Life/Samara

There are several mathematical structures and concepts that are described as "bootstrapping" themselves into existence. These systems typically rely on self-reference, recursion, or fixed-point theorems, where a structure is defined by its own properties, allowing it to "pull itself up by its own bootstraps." [1, 2, 3, 4]

Here are the primary examples of mathematical structures that bootstrap themselves:

1. Tupper's Self-Referential Formula

This is a famous formula that plots a graph of itself. [1, 2]

• How it works: It is a 2D inequality:
  
  
  
  
  
• The Bootstrap: When this formula is graphed over a specific 543-digit integer constant \(k\) in the \((x, y)\) plane, the resulting black-and-white pixels produce an image of the formula itself. The formula generates the very visual pattern that defines it. [1, 2]

2. The Constructible Universe (\(L\)) in Set Theory

In axiomatic set theory, the Constructible Universe (\(L\)) is a model of Zermelo-Fraenkel set theory (ZF) that is built up by iterating the definition of "definable subsets" through all ordinal numbers. [1, 2]

• The Bootstrap: Every countable model of set theory \(M\) can embed itself into its own constructible universe, \(L^{M}\). This means the structure \(L\) defines a model that is a submodel of itself, providing a structured, hierarchical form of self-generation. [1, 2, 3]

3. Self-Referential Sets (Anti-Foundation Axiom)

Traditional set theory forbids a set from containing itself (\(A \in A\)). However, using an Anti-Foundation Axiom (AFA) instead of the Foundation Axiom (FA), one can create "non-well-founded sets" that bootstrap themselves. [1, 2, 3]

• The Bootstrap: AFA allows the existence of a set \(x\) defined by \(x = \{x\}\). This is a self-referential definition that is perfectly consistent, representing a set that is solely composed of itself. [1, 2, 3]

4. Mathematical "Quines" and Fixed Points

A quine is a program that produces its own source code as its only output. In mathematics, this corresponds to fixed-point theorems. [1, 2]

• How it works: According to the Recursion Theorem in computability theory, any consistent, sufficiently complex system can define functions that call themselves (recursive functions).
• The Bootstrap: The system defines a fixed point \(x = f(x)\), where the structure \(x\) is defined entirely by its relationship to the function \(f\). [1, 2]

5. Theoretical Physics: The "Bootstrap" Approach

In theoretical physics, which is rooted in mathematics, the "bootstrap" conjecture suggests that the fundamental laws of nature are the only consistent set of equations possible. [1]

• The Bootstrap: Particle scattering amplitudes can be constructed by forcing self-consistency conditions (like unitarity). It turns out that string theory, for example, can be derived not from arbitrary assumptions, but as the only mathematical structure that satisfies these strict self-consistency conditions—it bootstraps its existence from consistency. [1, 2]