April 09, 2026 ·
Continuing on the recent trail where I learn for the first time about Immanuel Kant, I heard the discussion between Stephen Wolfram and Luz Christopher Seiberth yesterday which I thought was tremendous. Philosophy can get annoyingly vague really quickly and jumbled up even further when multiple people add commentary to it, so I am enjoying doing things in my own silly way trying to make sense of it all. Of course it'd be easier for me to just pick up a book and actually read Kant. But who's kidding who, I'm not doing that.
There was a lot of good stuff said in there but my main takeaway was about the distinction Kant drew between phenomenal and noumenal worlds; being idea-space and the real-world, roughly speaking. Fast forward, Wolfram refers to computational irreducibility as a set of experiences that cannot be modeled upfront and must be experientially gained. In other words, computer programs in contrast to math equations cannot jump ahead to solve for x or whatever answer; we must run the program to find out what happens when it runs. Math equations on calculators are computationally reducible in contrast to this set of computationally irreducible programs we experience.
Lecturing birds how to fly.
This stands as a frequent point of confusion because the most common assumption and criticism of computational thinking I come across is that people involved in it are trying to model the world in a mechanistic or mathematical way, wanting to reduce people and experiences to equations. On my end that sounds like a very 1600s view and criticism of it all. The missing piece is irreducibility, but even more specifically computational irreducibility. The thing to realize here is that reality itself is irreducible with pockets of reducibility in it, as Wolfram puts it. I imagine it as Swiss cheese. Meaning most of the time we cannot shortcut our way through reality, but every now and then we find spaces in which we can shortcut our way through a calculator or some tool like that.
An example: economists are always fighting whether markets are efficient or inefficient. I'm so over it. These words can be replaced with reducible and irreducible and it gives us a massive upgrade in understanding how they're both simultaneously. My conjecture is that markets are mostly inefficient with pockets of efficiency in them that get exploited soon after they're discovered. Like Swiss cheese. Ed Thorp talks about this. AI bots will be unable to get ahead of irreducible pockets for that very reason; in markets, in science, in everything.
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