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I am perpetually annoyed by the argument "the Sun's rays are parallel" made here and many other places. They tell you to take a single point on the sun, and dra

I am perpetually annoyed by the argument "the Sun's rays are parallel" made here and many other places. They tell you to take a single point on the sun, and draw a big skinny triangle from there to different points on the Earth, showing that the angle is very small. But any child can look at the sun (with eye protection :) and see that it is a disc, not a point of light. The disc is about 0.5 degrees, which is not so small. So, two rays emanating from opposite ends of the Sun and arriving at your eye are clearly not "effectively parallel." Of course, 0.5 degrees often is small enough to not matter in some contexts, but it's just annoying to me that the "start from a single point on the Sun" reasoning is used to draw a conclusion that flies in the face of simple observation. Sorry, rant over (:

jacobolus 2y ago
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.
deleted 2y ago
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doubloon 2y ago
electrons flow in a wire acceleration is constant light travels at c and other lies. the whole thing is a sham i tell you!!
- bigdict 2y ago
  electrons _do_ flow in a wire?
  - ForOldHack 2y ago
    According to which set of physical laws?
    - bigdict 2y ago
      those of our universe
drewhk 2y ago
> But any child can look at the sun (with eye protection :) and see that it is a disc, not a point of light. The disc is about 0.5 degrees, which is not so small. Page 11-12 explicitly discusses "sun-as-a-disk", the resulting shadow penumbra and other sources of inaccuracies.

jacobolus 2y ago

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.

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doubloon 2y ago

electrons flow in a wire acceleration is constant light travels at c and other lies. the whole thing is a sham i tell you!!

bigdict 2y ago
electrons _do_ flow in a wire?
- ForOldHack 2y ago
  According to which set of physical laws?
  - bigdict 2y ago
    those of our universe

drewhk 2y ago

> But any child can look at the sun (with eye protection :) and see that it is a disc, not a point of light. The disc is about 0.5 degrees, which is not so small. Page 11-12 explicitly discusses "sun-as-a-disk", the resulting shadow penumbra and other sources of inaccuracies.