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It's much easier to solve physical problems when you make as many simplifying assumptions as possible. These reduce the complexity of the problem and the amount

It's much easier to solve physical problems when you make as many simplifying assumptions as possible. These reduce the complexity of the problem and the amount of error-prone bookkeeping, without, in context, materially affecting the outcome. We all inevitably make a wide variety of assumptions of this type constantly when we work with any real-world system. They are a basic requirement for doing science and engineering. Literally every achievement of our technological society is built on top of a heap of simplified models of reality which are imperfect but usually good enough for the purpose demanded of them. We should celebrate them rather than moaning about them. And then, in the appropriate context where it is meaningful, we can peel back our models and examine a richer situation.

turtledragonfly 2y ago
Oh absolutely. I have no objection to the approximation. I have an objection to the shoddy reasoning put forth in its favor. If they said "0.5 degrees is small enough to ignore in this case" that would be fine. But instead they give this argument about how the angle is 0.00138 arc seconds, when that's clearly not the full story.
- lupire 2y ago
  What chapter has that? I didn't see it searching the gitlab.
  - turtledragonfly 2y ago
    I was talking about page 10 of the PDF [1], in Chapter 1 (odd, the original link in this HN post is now taken down). The part starting: "The rays of the Sun falling on the Earth can be considered parallel because..." As another commenter pointed out, the following paragraphs do mention the penumbra and solar disk, but I feel like the reasoning put forth in that initial paragraph is simply wrong (though common), even if it's briefly expanded upon afterwards. Or maybe it's just an artifact of the translation that it comes across sounding more authoritative than it is. [1] https://gitlab.com/mirtitles/perelman-geometry/-/raw/master/perelman-geometry.pdf https://gitlab.com/mirtitles/perelman-geometry/-/raw/master/...
    - alisonkisk 2y ago
      It's not wrong. It's just casually presented and not perfectly precise. the Chapter is about applting geometry in the real world, not idealized mathematical models. It is standard in empirical science to focus on first order effects, and then to address 2nd-order effects, which the book does in the following pages. Page 10 is a talking about how the angle of shadow is independent of subject position (human or pole), on the order of ~10m, and so we can treat all shadows at the same moment in time in the local area as similar. (Obviously shadows are not similar when comparing someone in Russia to someone in Mexico at the same time.) This is in contrast to a shadow from a streetlamp, where the angle changes from 45 degrees to 80 degrees over the span of a few meters of relative subject position. This is true, and the 0.5-degree error due to the size of the sun is not important to the overall result, which is already appromixate to a similar level of precision, and is the same for all subjects.

turtledragonfly 2y ago

Oh absolutely. I have no objection to the approximation. I have an objection to the shoddy reasoning put forth in its favor. If they said "0.5 degrees is small enough to ignore in this case" that would be fine. But instead they give this argument about how the angle is 0.00138 arc seconds, when that's clearly not the full story.

lupire 2y ago
What chapter has that? I didn't see it searching the gitlab.
- turtledragonfly 2y ago
  I was talking about page 10 of the PDF [1], in Chapter 1 (odd, the original link in this HN post is now taken down). The part starting: "The rays of the Sun falling on the Earth can be considered parallel because..." As another commenter pointed out, the following paragraphs do mention the penumbra and solar disk, but I feel like the reasoning put forth in that initial paragraph is simply wrong (though common), even if it's briefly expanded upon afterwards. Or maybe it's just an artifact of the translation that it comes across sounding more authoritative than it is. [1] https://gitlab.com/mirtitles/perelman-geometry/-/raw/master/perelman-geometry.pdf https://gitlab.com/mirtitles/perelman-geometry/-/raw/master/...
  - alisonkisk 2y ago
    It's not wrong. It's just casually presented and not perfectly precise. the Chapter is about applting geometry in the real world, not idealized mathematical models. It is standard in empirical science to focus on first order effects, and then to address 2nd-order effects, which the book does in the following pages. Page 10 is a talking about how the angle of shadow is independent of subject position (human or pole), on the order of ~10m, and so we can treat all shadows at the same moment in time in the local area as similar. (Obviously shadows are not similar when comparing someone in Russia to someone in Mexico at the same time.) This is in contrast to a shadow from a streetlamp, where the angle changes from 45 degrees to 80 degrees over the span of a few meters of relative subject position. This is true, and the 0.5-degree error due to the size of the sun is not important to the overall result, which is already appromixate to a similar level of precision, and is the same for all subjects.