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Reminds me of the concept of games in combinatorial game theory, they are a superset of surreal numbers (which are themselves a superset of the real numbers) in
by shemii 3y ago
Reminds me of the concept of games in combinatorial game theory, they are a superset of surreal numbers (which are themselves a superset of the real numbers) in which the definition of the surreal numbers is loosened in a way which looses the property of they being totally ordered. This creates games (read weird numbers) which can be "confused with" or "fuzzy" with other numbers, the simplest example is * (star) which is confused with 0, i.e. not bigger or smaller than it, it's a fuzzy cloud around zero (notated 0║*). More complex games called switches can be confused with bigger intervals of numbers and are considered "hot". By creating numbers from switches you can create even more interesting hot games.
- cosmojg 3y ago> By creating numbers from switches you can create even more interesting hot games. Well, don't leave us hanging! What are some of your favorite hot games on top of switches?
- shemii 3y agoI'm just starting to learn about all this stuff, but iirc thr game of Go is famously "hot". Also I will emphasize thats when talking about "games", usually what is meant is a game position. What spe cific game you are playing isn't too important as it can be shown that some positions in different games are equivalent.
- Akronymus 3y agoHeres a relevant video on the topic: https://www.youtube.com/watch?v=ZYj4NkeGPdM https://www.youtube.com/watch?v=ZYj4NkeGPdM I really love that video.
- shemii 3y agoExactly this video made me read more into this topic, I'm currently reading winning ways and lessons in play simultaneously. It's quite fun! I've just gotten started and am looking forward for what's left.
- __MatrixMan__ 3y agoThanks for sharing this. I just discovered it now and I love it too. The space of possible abstractions for any given phenomenon is vast, yet we almost always just assume that real numbers will do the trick and then begrudgingly allow complex ones when that doesn't work. If we're not lucky we end up with the wrong tool for the job, and we haven't equipped people to continue the exploration. It's a bias with some pretty serious consequences (thanks... Newton?). I don't think I've seen the inadequacy of number-systems-you've-heard-of demonstrated so clearly as it is done here.