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https://www.askamathematician.com/2013/01/qhow-do-lenses-tha...

https://scienceblogs.com/builtonfacts/2010/05/27/solar-heat-...

>Specifically, I feel certain that one can start a fire with sunlight reflected from a room temperature mirror, and don't understand the difference between a mirror and the moon within Munroe's argument.

A mirror does specular reflection and thus conserves the etendue of the sunlight. You're concentrating the image of the sun in the mirror, not light from the mirror itself.

The moon in contrast is mostly a diffuse reflector - it scatters most of the light that falls on it (and absorbs and re-emits most of the rest), so it is effectively a new light source.

Yes, I can agree with that. The problem for me is fitting it into Munro's argument. He says (in boldface): "You can't use lenses and mirrors to make something hotter than the surface of the light source itself".

This is true for a black body, but is it always true for an object being illuminated by another? I'm don't know that we can consider a diffuse reflector with a surface temperature of 100C as being equivalent to a black body with temperature of 100C. I think his conclusion is likely true (the moon is too dim to start a fire even with a really big magnifying glass) but I don't think he's right to point to the surface temperature of the moon as being the evidence of this conclusion.

Assume the sun was much brighter, so that ignition on earth is possible with a sufficiently large magnifier. Presumably if the moon was the same, this would mean the surface temperature of the moon was much higher. Now change the moon to be more heat conductive (causing the surface temperature to drop due to more heat loss on the dark side), and more reflective (causing the surface temperature to drop further due to less absorption). I'd guess that if you tweak the parameters sufficiently, you could end up with a surface temperature low enough that Munroe's argument would say that ignition is impossible, even though we've increased the intensity of the moonlight over our baseline.

How does Munroe know that we aren't in that second regime? I don't think there's enough information in his argument to distinguish. Alternatively stated, we know that there is some current temperature to which we can heat an object using concentrated moonlight. We also know that if we can change the shape and composition of the moon, we can reduce the surface temperature without reducing the intensity of moonlight. Unless there is some limit to the effectiveness of the heatsink that we can put on the moon, I think this means there is some possible arrangement that violates the assumption that the surface temperature must always exceed the temperature achievable with a magnifying glass.

(Thanks for helping me to puzzle this out)

An excellent point!

>Now change the moon to be more heat conductive (causing the surface temperature to drop due to more heat loss on the dark side),

Yeah, although this isn't too big in the case of the moon (unlike the Earth, it doesn't have an atmosphere and doesn't rotate rapidly, so there isn't too much redistribution of heat across its surface), it is definitely something that would confound the calculations. We'd still be able to just look at the effective temperature of light falling onto the moon and that would limit the temperature that we could light the object up to. But we wouldn't be able to use a direct measurement of the temperature of the surface of the moon.

> and more reflective (causing the surface temperature to drop further due to less absorption).

To the extent that it's a gray body (and most objects are approximately graybodies), this wouldn't actually lower the temperature. Absorptivity < 1 causes it to absorb less energy from the light, but for a gray body emmisivity equals absorptivity so it also radiates out less light too, and you actually end up reaching the same equillibrium temperature as fully absorptive black body.

Thanks for the kind response. I now see that the final average core temperature should remain the same, but I'm less sure about the surface temperature. There are a lot of complex processes involved, and I'm not sure that one can conclude that everything cancels out to keep the answer constant.

I respond late to offer a link (that's hidden on the second page of this thread) that I think presents that argument I was trying to make better than I managed to: https://physics.stackexchange.com/questions/370446/is-randal.... I thought the comments on the answer were a helpful reframing of the problem.

"Appeal to authority" is a fallacious rhetorical tactic only in an extraordinarily rigorous epistemological context, in which all truths need to be established from first principles. In practice, especially given the information asymmetry between the people that have devoted rigorous study to a thing and the people that think they know about it because making computers do things means they're smart (which is an intellectual pathology that I think ought to bother anyone who cares about the process of modeling physical phenomena accurately and honestly, even if it doesn't bother you), an argument like "physicists uniformly agree on this physical property" is a perfectly adequate assertion in favor of the claims made in the article. It would for sure be bolstered by the inclusion of sources, but you have to admit that you're throwing away a lot of relevant information towards the end of supporting your intuitive sense about how the optics here work. It's not impossible, in the absence of an argument from first principles to counter, that you're correct and that people who have formally studied physics and/or are familiar with the literature are wrong or misguided, but it sure isn't the most likely case by a wide margin. In that context, your certainty ("I don't think the details of his argument can be [correct]") seems much less well-founded.

I agree on most of your points. There is nothing inherently wrong with an appeal-to-authority in this case. If any substantial number of "reliable" physicists have looked at this problem, and if they unanimously agree that there is no way to concentrate light reflected from an object to produce a temperature greater than that object, then my intuition is almost definitely wrong and their conclusion is almost definitely right.

The nice part about physics though (like Munroe, I was also an undergraduate physics major) is that in simple cases like this, a suitable expert can usually defend their position with an argument comprehensible to a nonspecialist outsider. My doubt in this case is not that the experts are wrong, but that the experts haven't actually looked at the details of Munroe's argument and stamped it as "approved".

I think the part I find "offensive" is that CydeWeys is not claiming to be an expert himself, but is claiming to have certainty in what the experts believe. I don't know exactly why I find this offensive, but I do. And yes, this may be a problem with me, and not with CydeWeys' argument. I would not be offended in the same way by someone claiming "I am an expert and I approve this argument". Still, my question to him is genuine: what gives him this certainty?