(2022-03-18) Brander Possibility Space

Gordon Brander on Possibility space. In The Library of Babel (1941), Jorge Luis Borges imagines a strange world

The complete set of permutations of all letters fitting within 410 pages.

Incidentally, a complete set of permutations is called a derangement—a permutation that leaves no element in its original position.

There are other Libraries of Babel. In one corner of the multiverse, we find Borges’ Library, containing all possible combinations of letters

From Why Greatness Cannot Be Planned, by Kenneth Stanley, Joel Lehman (2015):

The nice thing about thinking of discovery in terms of this big room is that we can think of the process of creation as a process of searching through the space of the room. As you can imagine, the kind of image you are most likely to paint depends on what parts of the room you’ve already visited. If you‘ve never seen a watercolor, you would be unlikely to suddenly invent it yourself. In a sense, civilization has been exploring this room since the dawn of time

In this way, artists are searching the great room of all possible images for something special or something beautiful when they create art. The more they explore the room, the more possibilities open up.

Possibility spaces. Kenneth Stanley and Joel Lehman are AI researchers, and this is how an AI researcher sees creativity.

There is something powerful about this notion of possibility spaces, both from a theory standpoint, and as a way of seeing. It causes you to approach challenges in a different way. You don’t need to be creative. The creative breakthrough already exists out there in the space of possibility. It’s just waiting to be discovered.

This way of seeing can be applied to many problem spaces. Evolutionary biologists can think of the possibility space of traits as a fitness landscape, or the possibility space of shapes and forms an organism can take as a morphospace. AI researchers can think of the loss function of an algorithm as making up a loss landscapes.

Maybe I don’t have to cover all of this ground myself? Maybe other explorers can map it out too? Maybe a computer can even help me explore it?

Note that Borges’ Library of Babel is not infinite

DNA has no such limit. The chain can always get longer. So, life is open ended, unlimited. Nature is endlessly finding new ways of being alive.

But not all replicators are unlimited. Interestingly, it seems likely that within the murky origins of life, the process becoming life was once limited, not open-ended

Becoming unlimited was a major transition in evolution.

Note the powerful idea buried in this excerpt, mentioned in passing: there is a connection between modularity, composability, and open-endedness.

Another book. The book of Minecraft worlds: Mike Cook: Generative and Possibility Space. (2019)

Yet even this book does not contain all possible Minecraft worlds.

So there’s the set of things that are possible in Minecraft, and the set of things that are reachable via the generator engine.

The space of the possible and the space of the reachable.

Here are some questions I’m asking myself as I think about possibility spaces and tools for thought... (see his list)