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This is called “irrational mathematical efficiency”. Physicist Eugene Wigner coined the phrase in the 1970s to describe the interesting fact that natural phenomena, from planetary motion and strange behavior of fundamental particles to the impact of two black chasms billions of light-years away They can surprisingly be described and predicted by manipulating only numbers. Now let’s see if mathematicians can do what others have not been able to do: discover what makes us contemplate the laws of nature.
The task is not small. The question of how matter creates experience is one of the most difficult. Therefore, it is not surprising that early mathematical models of consciousness sparked a debate about whether they could show anything intelligent at all. But for a deeper look, mathematicians who develop autonomous tools face astonishing conclusions.
No less important, it shows that if we want an accurate description of consciousness, we may have to abandon intuition and accept as fact that a variety of inanimate objects may be conscious, perhaps even the universe itself. “This could be the beginning of a scientific revolution,” says Johannes Kleiner, a mathematician at the Center for Mathematical Philosophy in Munich, Germany.
If so, such thinking has matured long ago. Philosophers have been studying the nature of consciousness for at least a couple of millennia, mostly to no avail. Then, half a century ago, biologists arrived. They discovered correlations between brain cell activity and individual experiences called quality *. But the sad truth is that neuroscience hasn’t come close to answering the question of how neurons cause joy or anger, or the smell of coffee.
Brain activity
This is what the philosopher David Chalmers called a “serious” problem of conscience. Its unique complexity comes from the subjectivity of the very nature of sensory experience. Whatever it is, it is not a created and measurable thing. A philosopher called conscience a “ghost in a car,” and some people think we won’t scratch it from there.
But, as Wigner points out, there is no shortage of difficult problems on the math merits list. This stems from their ability to convert concepts into formal and logical statements that can provide information where nothing is seen when speaking confusingly only in human language. “It can help quantify the experience, for example, the smell of coffee, since we can’t speak English,” says Kleiner.
That is why he, and Oxford University mathematician Sean Tull, set out to mathematically formalize the former and, so far at least, the only theory of consciousness. Integrated Information Theory (IIT) was developed more than a decade ago by Giulio Tononi, a neuroscientist at the University of Wisconsin. His essential idea is that system consciousness arises from the flow of information between subsystems.
It is conceivable that these subsystems are islands and that each has a population of neurons. The islands are connected by flows of information traffic. For awareness to emerge, the flow of information must be complex enough for the islands to become interdependent, Tononi said. Changing the flow of information from one should change the state of the other. In principle, this can be used to provide degrees of awareness: measuring how well an island performs depends on information from other islands. This indicates how well the system integrates the information, and this value is denoted by “φ” (fi).
If there is no dependency between the information flows between islands, φ is zero and there is no consciousness. But if the deletion or termination of the connection affects the amount of information that the system combines and provides, then these groups φ are more than zero. The higher the φ, the more conscious the system will be.
Another important feature of IITs, called the insurance postulate, is that a group will only express awareness when it is “maximum.” That is, your own degree of consciousness must be greater than the degree of consciousness that can be attributed to any part of the system, and at the same time greater than the degree of consciousness of any system of which it is a part. For example, any and all parts of the human brain may have mini-consciousness. But when the consciousness of a part increases, say, when a person returns from anesthesia, this mini-consciousness is lost. In the case of IIT, only the system with the largest φ shows awareness, which we perceive as experience.
The idea got supporters as soon as Tononi proposed it. “Theoretically, it is quite attractive,” says Daniel Bor of the University of Cambridge. “There is such a connection between consciousness and mind: beings who can recognize themselves in the mirror also seem to be the most intelligent. So some connection between consciousness and mind seems logical. ” And the mind also has a connection to the collection and processing of information. “This means, it can be said, that consciousness is related in some way to the processing and integration of information,” says Boras.
It seems significant and based on what we know about consciousness in the human brain. It suffers when, for example, the cerebral cortex is damaged. In this region there are relatively few strongly interconnected neurons, and they under the IIT are large. Meanwhile, there are many more neurons in the brain, but they are not related. According to the IIT, brain damage could be predicted to have little effect on the experience of consciousness, and research shows exactly that.
On closer inspection, however, the IIT is not as convincing. For example, φ should decrease when we are asleep or under anesthesia, but Bor’s work in the laboratory shows that this is not the case. “Increase or remain the same,” he says. And explaining why the flow of information causes a sensation like the smell of coffee is problematic. The IIT defines conscious experience as the result of “conceptual structures” formed by the location of the relevant parts of the network, but such an explanation seems to be too complex and insufficient for many.
Philosopher John Searle does not like IIT. He argues that this theory ignores the question of cause and mode of consciousness, and makes the dubious assumption that it is simply a by-product of the existence of information. As a result, he said, the IIT “doesn’t look like a serious scientific proposition.”
Perhaps the most serious criticism of IIT as a mathematical theory is the ambiguity of the numbers used. To calculate the importance of a complex system like the brain, the IIT provides a recipe that is practically impossible to follow, even Tononi himself acknowledges.
“Based on the current description, it is very difficult to calculate the total brain,” says Tull. And that’s a very nice saying. The researchers found that calculating 86 billion human brain neurons φ with the current method would take longer than the age of the universe. Bor discovered that it would take 5 × 10⁷⁹ years to calculate the 302 neurons of a nematode worm with a standard computer.
And calculating φ for things where consciousness is not expected to be discovered produces very strange results. Scott Aaronson, a physics theorist at the University of Texas at Austin, for example, was initially fascinated by this theory, which he describes as a “serious and honorable attempt” to discover when the question of what physical systems are conscious can be understood. in an understandable way. But then he started to review it.
Aaronson calculated the mathematical object called the Vandermonde matrix, φ, based on the IIT principles. These are number grids whose values are interdependent and can be used to create circuits called Reed-Solomon decoding circuits to correct errors in the information read from CDs and DVDs. He discovered that Reed-Solomon chains large enough φ would be huge. Increasing that chain would eventually make her much more conscious than a human being.
The same problem arises with other ways of processing information, emphasizes Aaronson: information can be integrated, its importance is enormous, but it does not result in something that we could call consciousness. He concludes that the IIT inevitably predicts a large number of consciousnesses in physical systems that no person in their right mind would consider “conscious” at all.
Aaronson has given up on the idea, but not all highly conscious circuits seem inappropriate. For Kleiner, he interprets this as a consequence of the nature of consciousness: we lack information because we support any analysis of consciousness with introspection and intuition. “We cannot receive messages from the circuits,” he says. “That’s the problem.”
In his opinion, instead of rejecting the perspective model, the underlying mathematics should be clarified and simplified. Therefore, he and Tul are preparing to discover the necessary mathematical ingredients of IIT by dividing it into three parts. First is the set of physical systems that encode information. Then there are various manifestations of conscious experience, or in other words, “spaces.” And finally, there are the first two basic components of connection: the “repertoires” of cause and effect.
In February, they published a preliminary article showing how these ingredients can be combined in a logically consistent way to apply the IIT algorithm to find φ. “The fundamental idea is now well defined enough to avoid technical problems,” says Kleiner.
They are inspired by mathematicians now being able to develop more advanced models of consciousness based on IIT, or better yet, on competitive theories. “We would be delighted to contribute to the further development of IIT, but we also hope to help improve and unify the various existing models,” says Kleiner. “Then maybe we will even offer new ones.”
One of the consequences of such a stimulus may be the perception of the idea put forward by the IIT adaptation networks that inanimate matter can be conscious. Such a statement is generally immediately rejected because it seems to argue in favor of “panpsychism,” the philosophical view that consciousness is a fundamental characteristic of all matter. What if you have walkie-talkies?
It is understandable that no one says that the fundamental particles have feelings. But panpsychists argue that they can have a small, albeit small, level of consciousness, which, when combined, can create different levels of consciousness that are studied by birds, chimps, or us. “Particles or other basic beings may have simple forms of consciousness that are fundamental, but complex human and animal consciousness would form or derive from them,” says Hedda Hassel Mørch of the University of Applied Sciences of mainland Norway, Elverum.
The idea that electrons can have consciousness may not be easy to accept, but panpsychists argue that this is the only way to solve a difficult problem: instead of trying to explain consciousness in terms of nonconscious elements, we should ask ourselves how rudimentary forms of consciousness can cause our complex consciousness.
With that in mind, Mørch believes that the IIT is at least a good start. Her general approach of analyzing firsthand what we feel, activating certain areas of the brain and using it to determine the limits of what her physical counterpart may be is “probably correct,” she says. And although the current wording of the IIT does not strictly establish that consciousness belongs to everyone and everything, since consciousness is found in networks and not in individual components, it is very possible that a purified version of it can do so. “I think IIT’s core ideas are perfectly in line with panpsychism,” says Kleiner.
This may be consistent with other indicators that show that the relationship between our consciousness and the universe may not be as direct as we imagine. Suppose the problem of quantum measurement. Quantum theory, by which we describe the basic interactions of matter, states that an unmeasured quantum object can have many different meanings, described by a mathematical entity, called a wave function. So what collapses the many possibilities into something definite and “real”? In one opinion, this is done by our consciousness, which would mean that we live, as physicist John Wheeler put it, in “participation in the universe.”
This idea raises many problems, among which is the question of what caused the collapse before conscious minds developed. A suitable mathematical model in which consciousness can be a property of matter would at least provide you with a solution.
There is also the idea of Oxford University mathematician Roger Penrose that our consciousness is “the reason the universe exists.” It is based on an instinct caused by the deficiencies of quantum theory. But if this idea is supported in any way, the structure of the IIT, and, more specifically, its prohibition principle, establishes that the flow of information between the contents of the universe at all scales can create different consciousnesses that swell and flow, depending on what exists at any given time. Thus, the development of our consciousness could, in IIT terms, “ban” consciousness from the universe.
Or maybe not. There is good reason to be skeptical about the power of mathematics to interpret consciousness, not to mention the emerging side effects of understanding physics. It seems like we’re dealing with something so connected that, according to Phil Maguire, a computer scientist at the University of Maynooth in Ireland, calculations may even be impossible. “The collapse of the cognitive process is so complex that it is impossible to do so,” he says.
Others express similar doubts, including about the suitability of mathematics for this task. “I think mathematics can help us understand the neural basis of brain consciousness, and maybe even machine consciousness, but something will inevitably go overboard: feeling the inner quality of experience,” says Susan Schneider, a philosopher. and cognitive researcher at the University of Connecticut.
Philip Goff, a philosopher at Durham University in the United Kingdom, is of the same opinion. Consciousness is managed by physical phenomena based on its perceived properties, he notes, such as the smell of coffee or the taste of mint, which cannot be transferred to a purely qualitative objective model. “In explaining consciousness, standard scientific tools alone (public observations and mathematics) are not enough,” says Goff.
But Kleiner does not give up. Develop a mathematical model that can incorporate inexpressible personal experiences. It is now being revised. And even if it doesn’t work, something else will work, he says, “I am absolutely convinced that, along with experimentation and philosophy, mathematics can help us make significant progress in revealing the secret of consciousness.”
INTEGRATED INFORMATION
He argues that consciousness arises from how information moves between different regions of the brain, or different parts of any system. It seeks to provide an opportunity for awareness by evaluating how well the system integrates information.
GLOBAL NEURON WORKSPACE
It states that consciousness occurs when one part of the brain is transmitted to another. If the cerebral cortex decides that the information it receives is important enough, it sends a message to a broader network called the “global workspace,” hence the experience.
FOCUS SCHEME
He rejects the assumption that consciousness is a kind of “ghost in the machine” and offers a mechanistic explanation: it is the product of how the brain is modeled, focusing on the outside world or its internal states.
PREDICTIVE TREATMENT
The brain is considered a predictive machine that expects sensory impulses to work as efficiently as possible. This idea is based on the fact that conscious experiences, including self-perception, are often based on our expectations and not on what they really are.
Michael Brooks
www.newscientist.com
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