https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From I haven’t read it but I’ve read enough from the ideas from it to find it agreeable. But I like Lakoff’s ideas generally, even if I may quibble on some specifics. Embodied cognition ‘grabbed me’ from the moment I heard about it.
If it’s been brought to Markov processes, now _that’s_ an area I understand much better. Somewhere I have a master chart of equivalent concepts between fields… I really should find it.
Nice! Hadn’t heard of Stone duality before. I’m a little more familiar with spectral spaces (only a little more) but I like where it’s going.
Generalizing to diplomacy, I believe it’s always possible to reach tentative agreement with just enough confidence to move forward.
How can diplomacy be modeled mathematically? Well, if it’s starting from a mathematical basis, already there is a common lingua, so partial agreement is already reached. There is a common field (language) to work within.
But then there’s contexts (with text) – what’s inbetween the words and lines, other language unaccounted for, that need resolution. Part of the problem with diplomacy is not everything is explicit.
So, you start from an empty Universe and go from there. Here’s empty Universe. What are all of the foundations that are built (that we are taking for granted) that lead to the point where there is disagreement?
One can also start from future and deconstruct backwards:
Let us assume AI has been reached and there is a working relationship between humans and AI. What aspects of human behavior have been modeled mathematically in the AI that allow diplomacy to occur in a fashion identical to human diplomacy?
Will this be a “better’ diplomacy than we have today (a more rational process that’s similar to advanced Game Theory? Or the same as today, complete with missed cultural differences and complexities?
Economics models are generally stoopid (I agree with that ) for as their basis, where are the rational agents? There were some real breakthroughs in the early 1990s when some mathematical modelling of human emotions were “added in”, leading to some better predictive abilities. [hence today, look at how much focus is on gathering “how does that make people feel?” statistics for marketing purposes].
I know this is off track from the direct direction you’re going in but when I see congruency symbols I think “metaphors” (particularly MAK Halliday’s Systemic Functional Grammar) and wonder “which level of metaphor do we find congruence between concepts?”
Or more simply, “how many dimensions “up” do I have to go in order to find congruence?”
I don’t think one has to create a new Universe to find congruence, although one *could* use David Kellog Lewis’s model if you need to. [but in those, the universes simply have no interaction and any similarities are counterparts that we can hypothesize about but never actually contact, nor they with us].
I think for most things for metaphors or (mathematical processes) to find congruence one just have to go up or down a few levels to reach it.
WAIT: let me scratch one word from what I said above
It’s difficult. It’s not “just have to”. It’s hard work.
Mathematical congruence is more specific… and I generalized to the overall concept of congruence I should get my head in math more. I’d entirely forgotten the importance of residue.
The temptation of it though. Everytime I end up at Hopf fibrations I get sucked in and start exploring. Months go by and one day I look up from my computer and go, “WHAT JUST HAPPENED?”
It’s potato chips. Math concept candy. It’s in the area of boundaries of systems which is one of my favorite areas and whenever I end up there I don’t leave for a while.