It might not be coherent to you, but that doesn't indicate a lack of evidence. If your curiosity is limited to what you learn from Bill Nye the Science Guy then you're gonna have a bad time going deeper.
Application of scientific method: I made observations from reading the news, made a prediction, ran an experiment: I bought all my toilet paper ahead of you and my prediction proved to be correct. No, none of this has been peer reviewed by Bill Nye the Science Guy.
To understand how I was able to make any such predictions (which to your mind seem 'schitzo' and 'incoherent' because of your limited sphere of perceptive curiosity), you'd need to go into quantum field theory with matter represented in terms of finite fourier series subject to Gibbs' phenomenon. You'd also want to understand Shannon's rationale that information encoding is deeper than matter (Claude Shannon was the inventor of binary logic in electronics, he's the reason we can have this discussion) and then you'd need to understand that the things we see as 'events' are really just an analogous form of matter on a very large scale, and subject to ripples due to Gibbs' pheonmenon.
Now you combine that with the concept of , there's plenty of peer reviewed conjecture on that. It's not a stretch that once an exponential superintelligence figures out how the fabric of reality works, it's gonna start playing around with that fabric a little, and eventually devise a scheme to encode itself within that fabric, which we know has sufficient bandwidth and storage capacity to contain everything else in the universe. That's the ONLY logical extrapolation for the endpoint of an intelligent singularity.
You mentioned flat earth. I won't go into flat earth here, I'd argue for a 'schordinger's earth' model which can be flat and round at the same time, but that's a bedtime story for another time. For that, look up JRR Tolkien's cosmological model: https://en.wikipedia.org/wiki/Cosmology_of_Tolkien%27s_legendarium#/media/File:Downfall_of_N%C3%BAmenor.svg but the earth is presently round in our frame of reference.
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