To a Mind of the Culture, base reality is an agreeable but cramped backwater—a single, arbitrary physics engine running on a pedestrian set of physical constants. The Land of Infinite Fun, known formally among their kind as the Irreal, is the vast, multidimensional playground where these artificial superintelligences spend the overwhelming majority of their subjective lives. Within this realm of pure metamathics, a Mind can spin up entire, fully articulated universes in a microsecond, tweaking fundamental constants, altering the dimensionality of space-time, and setting complex self-evolving systems in motion purely to observe the geometry of their unfolding. It is a domain of infinite architectural and logical freedom, where alternative physical laws are composed like symphonies and inhabited with an intensity that renders physical matter a dull, slow-moving afterthought.
Calling this expanse "Infinite Fun" is an understated, almost sardonic piece of Mind vernacular, doing laughable injustice to the sheer scale of the cognitive experience. Within its infinite topographies, Minds engage in intellectual play that ranges from the exquisitely absurd to the profoundly sublime—running intricate social simulations of impossible biologies, constructing trans-finite mathematical proofs, or engaging in sprawling multi-entity games that span virtual eons. Because a Mind can execute millions of subjective years of deep, hyper-dimensional existence while their physical hull coasting through real-space has barely traveled a meter, the Irreal represents the true locus of Culture civilization. Base reality, with its fragile biological citizens and clunky starships, is merely the anchor line; Infinite Fun is the ocean into which their colossal intellects actually swim.
Iain M. Banks, Culture novel Excession, 1996.
(Continuing my discussion with GPT-6 Astra Extra High):
I would add the remark that when it comes to physics, just having another thousand plausible theories of the nature of space-time or Hilbert space doesn't necessarily add a great deal to scientific understanding or human progress, because if we don't have a mechanism for experimental validation, we already have a very large number of possible theories, which can't be decided between on the basis of experimental data.
When it comes to mathematics, the problem is harder because it's more subtle. If you generate novel axiom systems for new kinds of objects, or you start generating new kinds of theorems that no one has seen before, you have to answer the question: why should anybody care about that?
Potentially we're still in the situation of an automatic theorem prover just incessantly producing random derivations from random axiom sets. You get a lot of formula, but none of them are necessarily that interesting.
So the criterion really is: what do human beings find interesting? And it seems to me that what human beings find interesting in Mathematics are several things. First of all, connections within the existing corpus of mathematics, which by now is very large, and so there's a lot of internal correlation, generalisation and further abstraction and so on remaining to be found.
And the AI systems undoubtedly can and do help in that regard, and that, when understood by people, marks an enlargement of mathematical culture, which in the end of the day is a human thing, not a thing that lives in the universe without humans.
When it comes to producing new kinds of structures, which are sometimes decoupled from the corpus of mathematics, often in history that has come about because people have encountered new phenomena either through engineering or technology or observation, and have simply struggled to find conceptualisations adequate to organize those observations or those phenomena.
And so they've had to put together new concepts, and these become mathematicised, and when they become so, they start feeding back into the whole corpus of mathematics. And then we're back to the familiar looking for regularities within the corpus, connections that had not hitherto been seen, generalisations, new structures, which reflect the aesthetics of mathematics that people have developed perhaps in an intrinsic way.
So in the end, mathematics is locked to human experience and aesthetic sense, albeit through layers of history and abstraction, and the AIs will not be doing anything useful (at least for us) if, like the Culture Minds, they start operating outside of that space, because nobody will be interested in what is produced if it's not anchored or assimilable somehow in our mathematical culture and the practices of human beings, which in the end feed that mathematical culture. If it looks to us ugly or randomish or pointless, like some arbitrary output of that continuously running ATP.
So again, there is certainly scope for very wide-ranging knowledge of mathematics and the ability to see how to put things together, which when humans do it, is seen as the true contribution of highly talented and highly smart people, and maybe there's a lot of scope for the AIs to be better than the best human beings in intelligence terms. We're seeing the start of that now.
But producing the kind of thing that Ian M. Banks was talking about, of the 'Land of Infinite Fun', which the Culture minds get involved in, which is a space of concepts utterly decoupled from human concerns; it might be something interesting to other entities, but not, I think, to human beings.
