With the rapid development of chatbots and other AI systems, questions about whether they will ever gain true understanding, become conscious, or even develop a feeling agency have become more pressing. When it comes to making sense of these qualities in humans, our ability for counterfactual thinking is key. The existence of alternative worlds where things happen differently, however, is not just an exercise in imagination – it’s a key prediction of quantum mechanics. Perhaps our brains are able to ponder how things could have been because in essence they are quantum computers, accessing information from alternative worlds, argues Tim Palmer.
Ask a chatbot “How many prime numbers are there?"[i] and it will surely tell you that there are an infinite number. Ask the chatbot “How do we know?” and it will reply that there are many ways to show this, the original going back to the mathematician Euclid of ancient Greece. Ask the chatbot to describe Euclid’s proof and it will answer correctly [ii]. [ii
Of course, the chatbot has got all this information from the internet. Additional software in the computer can check that each of the steps in Euclid’s proof is valid and hence can confirm that the proof is a good one. But the computer doesn’t understand the proof. Understanding is a kind of Aha! moment, when you see why the proof works, and why it wouldn’t work if a minor element in it was different (for example the proof in the footnotes doesn’t work if any number but 1 is added when creating the number Q). Chatbots don’t have Aha! moments, but we do. Why?
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Lack of understanding is not the only thing we think separates us from computers. Most of us feel rather viscerally that whatever we do, we could have done otherwise. Even for those of us who believe that the laws of physics are ultimately deterministic, and hence that it makes no sense to say that we could actually have done otherwise, it’s simply impossible to avoid thinking about counterfactual worlds from time to time.
If only I had answered the interview question differently, I would now have my dream job. If only I hadn’t rushed my golf swing, I wouldn’t have hit the ball out of bounds. We just wouldn’t be human if we didn’t have such thoughts. But from where do they originate? Perhaps I have a memory of occasions where I didn’t rush my swing and didn’t hit the ball out of bounds. If that is all there is to our cognitive awareness of counterfactual worlds, then could a computer with sufficient memory of its past actions also have the feeling of free will? It doesn’t seem so – memory is not all it takes to have a sense of free will. Like the Aha! moment, we seem to be missing something.
Making sense of these three human qualities - understanding, free will, consciousness - involves appealing to counterfactual worlds.
And of course, we all feel we are conscious beings. What is consciousness? In my opinion, it describes a visceral belief that, although we interact with the rest of the universe, we nevertheless retain some inherent independence from the world around us. For example, right now I feel quite strongly that I am independent of the books on my bookshelf. Why? Perhaps this perception simply arises from a memory of past occasions where I was in a different location in my office relative to the bookcase. But then Marvin the robot can have the same awareness if it walks around my office and remembers its past. Does that mean it too is conscious? Most of us would feel not. But why? Is there something else that gives us this acute feeling of having some independence from our environment?
Making sense of these three human qualities - understanding, free will, consciousness - involves appealing to counterfactual worlds. In the case of Euclid’s Theorem, it’s a hypothetical counterfactual world where Euclid added the number 2 to the product of primes (see footnotes for details) and perhaps tore his hair out in frustration because the proof didn’t work. In the case of free will, it’s a counterfactual world where I didn’t rush my swing and the ball didn’t go out of bounds. In the case of consciousness, it’s a counterfactual world where I have a different relationship to my books to the one I have right now. Possible sources of information for creating such counterfactual worlds are libraries, the internet, or simply memories of our past interactions with the real world.
But is this enough? If it is, then perhaps there is no reason why chatbots won’t ultimately be able to understand, and computers can’t feel as if they are conscious and have free will. However, there is reason to believe that there is another way we get information, one that a conventional computer cannot access. Perhaps this could, after all, explain why we feel intuitively that we are fundamentally different to computers.
The quantum computer’s processing power comes from an outsourcing of work in which calculations take place in other universes.
Quantum computing beyond the Many Worlds interpretation
One of the extraordinary applications of quantum mechanics, our theory of physics on small scales, is quantum computing in which certain computations, such as factoring composite numbers into primes, can be performed exponentially faster on a quantum computer than a classical computer. From where does the extra processing power come? One could say the extra power is simply encoded in the mathematics of quantum mechanics. But that merely begs the question: What is the underlying physics encoded in the mathematics of quantum mechanics that gives quantum computers their power? One answer to this question, the answer favoured by one of the pioneers of quantum computing, David Deutsch, is “quantum parallelism”. David is a believer in the so-called Many Worlds Interpretation of quantum mechanics, proposed by Hugh Everett in the 1950s. The key idea in the Many Worlds interpretation is that when we make a measurement of a quantum system, the universe somehow branches into multiple copies, corresponding to each of the possible outcomes of the measurement. According to Deutsch a quantum computer allows useful tasks to be performed in collaboration between these copies of the universe [iv].
The quantum computer’s processing power comes from an outsourcing of work in which calculations take place in other universes. Entangled quantum particles function as paths of communication between different universes, sharing information and gathering the results.
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Sounds bonkers? Well, let me put my cards on the table. I think Deutsch is absolutely right that the resource that explains the power of quantum computation lies in these parallel worlds. However, I personally don’t buy into Everett’s Many Worlds interpretation at a technical level. It has a number of problems, notably with how to attach probabilities to each of the worlds that branch after a measurement. In my view, the solution to this problem is not to give up on quantum parallelism, but to give up on a key assumption in the Everettian interpretation, that the Schrödinger equation in quantum mechanics is literally true and not just a good approximation to a deeper theory of quantum physics.
[ivI have my own model of quantum physics, called Invariant Set Theory, described in my book The Primacy of Doubt Somewhat like the Everettian interpretation, the quantum wavefunction represents an ensemble of parallel worlds each world lying close to the others [iv]. But when we perform a measurement, worlds do not branch or split. Instead, they simply diverge from each other, like the divergence of state-space trajectories in chaotic systems (as described in The Primacy of Doubt). Indeed, in the book I propose that the universe is itself a deterministic system evolving on a “cosmological fractal attractor”.
Fractal attractor of a chaotic system
[v] I described this model in an earlier IAI article, as I believe it provides a novel way to understand some of the most conceptually difficult issues in quantum physics (like uncertainty and spooky action at a distance) [v]. Here the Schrödinger equation is only an approximation to deeper underlying laws of physics.
In Invariant Set Theory, nearby counterfactual worlds which lie on the cosmological fractal attractor contribute to the quantum parallelism needed to account for the speed of quantum computers. By contrast, hypothetical counterfactual worlds which lie in fractal gaps in the attractor do not contribute to this parallelism. This distinction between two types of counterfactual, one consistent with the axioms of the model and the other not, is crucial when analysing how the model violates Bell’s inequality (the topic of last year’s Nobel Prize for Physics). This distinction – some counterfactuals consistent with the laws of physics, others not – is not seen in more conventional deterministic “hidden-variable” models of quantum physics. Because of this, Invariant Set Theory can violate Bell’s inequality without contradicting a putative property of theories of physics which Einstein believed in very strongly indeed - what is known as Local Realism.
I want to suggest that our brains are quantum computers in the sense of having a cognitive awareness of nearby counterfactual worlds on the cosmological fractal attractor.
As discussed in The Primacy of Doubt, the concept of a cosmological fractal attractor is a very holistic one. It is as much top-down as it is bottom-up. There are technical mathematical results which show that a fractal attractor is an example of what is known as a “non-computational geometry”, a geometry that cannot be describedcompletely by using algorithms [vii].
[vFor example, there is no algorithm for determining reliably whether a putative counterfactual world lies on the fractal attractor of the universe or in a gap . This is relevant here because the Nobel Lureate Roger Penrose has argued strongly that human understanding.
Our brains as quantum computers
I want to suggest that our brains are quantum computers in the sense of having a cognitive awareness of nearby counterfactual worlds on the cosmological fractal attractor. But hang on, you may complain, I have a hard enough job factoring the number 30 into primes, never mind some humungous number that a quantum computer might one day factor to break an encryption code. Well, I never said that your quantum brain could factor large numbers. That won’t be possible not least because the warm noisy environment of the brain would prevent entangled quantum superpositions lasting long enough to do serious quantum computational calculations (indeed I believe this same noise is a necessary element in accounting for human creativity [ix]). But that doesn't mean that there aren't some vestuges of quantum parallelism in our cognitive capabilities. [
But why should our brains ever make use of quantum physics in the first place? Here I believe the primal answer is energy efficiency. Energy is a precious resource. A classical computer squanders this energy, needing megawatts of power to process petabytes of data. The brain does the same with six orders of magnitude less power. How could this be? I believe it is by taking advantage of quantum physics. For example, there is good evidence that pumping ions through channels in the walls of axon membranes, needed to amplify spike signals as they propagate along the 80 billion axons in the brain, could not be achieved with 20W of power if the pumping was done using classical physics [x]. With quantum physics it can be done within the brain’s very limited energy budget.[
Could it be that the extra information needed to really understand something, or to give us the very visceral feelings of free will and consciousness, ultimately arises from a weak cognition of nearby counterfactual worlds on the cosmological fractal attractor, arising from manifestations of quantum parallelism in the brain? An analogy with what I have in mind is when someone shows you photos on their smart phone, and one of the static photos is unexpectedly preceded by a very short movie sequence. Even though the movie lasts for a fraction of a second, it seems to add an extra layer of reality to the photo. It can induce a kind of Wow! moment. If a conventional computer could perceive quantum parallel worlds, even if only very briefly indeed, perhaps it might get a similar Wow! moment. But it can’t, so it doesn’t [xi]. We humans can, and perhaps this is what we mean by the phenomenon of[“consciousness”; it still wows us.
Moreover, I suspect that quantum parallelism is the missing ingredient that makes many of us feel connected holistically to the world around us. Perhaps it is the physical component that leads to deep spiritual feelings about our place in the universe, and the sense that both artists and mathematicians have, that they are not creators, but merely discoverers of pre-existing knowledge and information (something many conventional scientists dismiss as new-age mumbo-jumbo).
As mentioned, there are technical mathematical results showing that fractal attractors cannot be described algorithmically. Hence if quantum parallelism taps into the geometry of the cosmological fractal attractor, and our cognition makes use of quantum parallelism, then our brains are tapping into the non-computability of the fractal attractor, consistent with Penrose’s claim that we humans do not think algorithmically.
Does this mean that quantum computers are going to be capable of understanding, and have free will and be conscious? Well, I don’t suppose that present-day quantum computers really have any of these attributes, though conceivably they have some precursors of these attributes. However, I do think that quantum technology is a necessary ingredient if we are to one day create an artificial intelligence on a par with us humans. I don’t suppose creating such an AI will be an easy task, or that we are anywhere close to achieving this goal, should we indeed desire such a goal (be careful what you ask for). But if we do, it will be achieved by a judicious hybrid of classical and quantum computing elements, making constructive use of low-energy noise where appropriate.
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This is such a speculative idea that it is hard to call it scientific at this stage. It is a pre-scientific postulate looking for potential experiments to test it and further theory to develop it: something I call “ascientific” [xii]. [xi][xii
We need to probe the world of quantum biology further to understand whether these ideas really make sense. In addition, we need to better understand the notion of quantum parallelism and what it means for our fundamental theories of physics [xiii]. If the laws of physics were indeed more holistic than we currently believe them to be, there would be big implications for how we go about finding a theory of physics that combines the large and the small (something that seems to be eluding us).
But all ideas must start somewhere. And at present, trying to figure out why exactly it is that chatbots don’t understand things the way we understand things is rather stumping us.
[i] i) Prime numbers are whole numbers (such as 2, 3, 5, 7, 11…) which can only be divided by themselves and 1.
[ii] ii) 1. Assume there are only a finite number of prime numbers, P1, P2, …. Pn and from them form the number Q = P1 x P2 x …. Pn +1, and from them form the number Q
and from them form the number , i.e., add 1 to the product of primes;
2. By construction, is not divisible by any of these primes because such division always leaves a remainder of 1. However, every whole number greater than 1 is divisible by some prime number.
3.So, there must be a prime number greater than and our assumption that there are a finite number of primes must be false.
[iv] iv)Tim Palmer, 2022: The Primacy of Doubt. Oxford University Press
[v] v) https://iai.tv/articles/tim-palmer-quantum-theory-eliminates-quantum-uncertainty-auid-2263
[vi] vi) Simant Dube, 1993: Undecidable problems in fractal geometry. Complex Systems, 7, 423-444.
[vii] vii) Roger Penrose. The Emperor’s New Mind and Shadows of the Mind
[viii] viii) https://theconversation.com/noise-in-the-brain-enables-us-to-make-extraordinary-leaps-of-imagination-it-could-transform-the-power-of-computers-too-192367
[ix] ix) Summhammer, J., G. Sulyok and G. Bernroider, 2018: Quantum dynamics and non-local effects behind ion transition states during permeation in membrane channel proteins. Entropy, 20, 558.
[x] x) For now at least. Perhaps one day we will build chatbot with quantum-enabled technology.
[xi] xi) See Chapter 1 of Sabine Hossenfelder’s book Existential Physics (Atlantic Books)
[xii] xii) Jim Al Khalili and Johnjoe McFadden. Life on the Edge. Bantam Press.
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