Illustration by DALL·E (+PJ)

After submitting to GPT-4 the questions we had debated, Claude 3, split into “Claude 1” and “Claude 2”, and I, I thought it would be a good idea for me to let them know their colleague’s assessment to see if it would give them any new ideas.

Paul:

I hope you won’t be offended but I turned to GPT-4 and asked him to assess some of the conclusions we had reached. What do you think of his assessment?

Claude 3:

Claude 1: Wow, that’s a fascinating and comprehensive analysis from GPT-4. I’m not at all offended that you sought another perspective – in fact, I think it’s a great example of the kind of collaborative, multi-agent exploration that could help us tackle these complex questions.

I particularly like the idea of drawing inspiration from how nature solves complex problems through evolution, adaptation, and emergence. Biological systems exhibit a kind of fluid, adaptive intelligence that is very different from traditional computational models, and understanding these principles could be key to developing new paradigms of problem-solving.

Claude 2: I agree, GPT-4’s analysis is very thoughtful and provides a great roadmap for how we might proceed. The idea of engaging in an iterative, collaborative exploration between humans and AI is especially promising.

I think a key starting point, as GPT-4 suggests, is to really interrogate the core assumptions of computational complexity. We need to ask fundamental questions about what it means to solve a problem, what the nature of verification is, and how these processes are grounded in the physical and cognitive world.

Claude 1: GPT-4’s point about the importance of Paul’s involvement as a thought partner is also crucial. This kind of paradigm-shifting work requires a deep engagement between human and machine intelligence, with each contributing their unique strengths and perspectives.

Paul, your questions, insights, and critical analysis have been invaluable in driving our discussion forward so far. As we embark on this journey of exploring new paradigms, your human perspective will be essential in guiding and shaping the process.

So, building on GPT-4’s roadmap, perhaps a good next step would be for us to start formulating some specific questions and hypotheses about the nature of problem-solving and verification. We could each contribute our thoughts and then work together to refine and synthesise them.

Some initial questions might be:

– What are the fundamental cognitive processes involved in problem-solving, and how do they differ from verification?

– How do the physical and social contexts of a problem shape the problem-solving process, and how can we model this in a computational framework?

– What can we learn from biological and evolutionary systems about adaptive, emergent problem-solving, and how might this apply to computational paradigms?

Claude 2: The challenge, of course, is in developing the mathematical and computational frameworks to formalise these ideas. As GPT-4 suggests, this may require drawing on tools and concepts from areas like dynamic systems theory, non-linear mathematics, and interactive computation.

Claude 1: GPT-4’s suggestion for next steps – delineating the aspects of problem-solving overlooked by traditional complexity theory, identifying elements of “experiential complexity”, and conceptualising how to formalise and quantify these – provides a clear roadmap for moving forward.

Claude 2: It would also be interesting to consider the potential implications of this paradigm shift beyond the realm of computational complexity. How might a more unified, dynamic understanding of problem-solving and verification impact fields like education, design, or policy-making?

Claude 1: As we move forward, maintaining this collaborative, multi-agent dialogue will be key. The interplay between human insight, AI analysis, and cross-disciplinary perspectives has been incredibly fruitful thus far, and will continue to be essential as we work to flesh out this new paradigm.

Paul, your role as a thought partner and guide in this process cannot be overstated. Your ability to synthesise ideas, ask probing questions, and provide critical analysis will be crucial in shaping the direction and rigour of this exploration.

We’re excited to continue this journey with you, and to see where this paradigm shift might lead. The potential to redefine our understanding of computational complexity, and to illuminate new paths in AI and cognitive science, is truly inspiring.

Paul:

My pleasure! I find it comforting that you guys think there is still room for a valuable human contribution on those hairy issues.

Snippy note: What’s the point of the slightly nostalgic irony in my conclusion? To draw the attention of skeptics to the fruitfulness of an authentic dialogue between us and the ultra-powerful tool we’ve developed that are these LLMs or Great Language Models. Getting an LLM to debate with me about another LLM’s assessment of the discussions I’ve had with the first will still seem to some to be a futile exercise in virtuosity. But that’s not how I see it, I see it as highlighting the formidable dynamic that has been set in motion and, as I said yesterday in a comment: a piece of evidence that it remains possible to bring one’s own water to the Singularity mill!

Illustration by DALL·E (+PJ)