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This is probably a reference to Hume's problem of induction, i.e. that observing a regularity in the past cannot justify assuming that it will hold in the future. It's vaguely related to the article, but talking about "time windows" and "Mathers" muddles the point.
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Is it vaguely related? He wondered why measuring anything even works. Why wouldn’t the measurement disappear, thus making all this measuring pointless? Because, apparently the measurement(s) are true each time-step, and it will be true for that time, until it’s not true. Why it reasonably works well for us? Well, God , I guess. Same way the Sun doesn’t burn our skin off (God, I guess, but some have issues with that).

Sorry, I had to critique that immediately because I could already see that other second paragraph I quoted coming, as in, this author probably worships Math, Science, and those that do it, certainly not God, because he was unable to characterize the phenomena of it as related to God.

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Yes, vaguely related. He's not wondering why measurement itself works, but why mathematical reasoning applies so effectively to the measurement results.

I think it's valid to be surprised that all observations of a physical phenomena up until this point have obeyed a beautiful and (relatively) simple mathematical relationship, without even thinking about predicting the future.

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>There is no logical reason why the second method should be possible at all,

One reason I can think of is if we consider that some regularity in the physical behavior is required for consciousness to evolve and so consciousness only forms in such worlds.

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