Thought for the Evening: Olbers' Paradox
Olbers' Paradox, also known as the dark sky paradox (and which, like many named things in science, was not discovered by the person after whom it is named), is, speaking roughly, the puzzle of why the sky is so dark at night. Suppose the stars go on forever. The farther out you go, the more stars there are; infinite stars, more or less distributed evenly, would result in every point of the visible sky being filled with light. The night sky would then have to be literally star-bright. The light from an infinite field of stars reaching us is a lot of light; it is obvious that that much light does not reach us.
The paradox arises from assuming a lack of limits on several things, so there are a few logically possible solutions one might propose to the paradox, all of which introduce some kind of limit. As things stood at the beginning of the twentieth century, those possible solutions seem to have been:
(1) The stars are finite in number
-- -- (1a) in infinite space that is therefore mostly starless.
-- -- (1b) in finite space.
(2) The amount of light able to reach us is finite
-- -- (2a) because it has had only finite time to travel
-- -- -- -- -- -- (2a1) as stars have a finite history in a universe with an infinite past.
-- -- -- -- -- -- (2a2) as stars have a finite history since the universe has a finite past.
-- -- (2b) because the spatial range of light is finite
-- -- -- -- -- -- (2b1) because over a long enough range it stops being light
-- -- -- -- -- -- -- -- -- -- (2b1a) because it dissipates.
-- -- -- -- -- -- -- -- -- -- (2b1b) because it becomes indiscernible or unmeasurable.
-- -- -- -- -- -- -- -- -- -- (2b1c) because it becomes something else.
-- -- -- -- -- -- (2b2) because it is obstructed
-- -- -- -- -- -- -- -- -- -- (2b2a) by some material.
-- -- -- -- -- -- -- -- -- -- (2b2b) by some kind of structure or folding in space itself.
Assuming that the history in Jaki's The Milky Way and The Paradox of Olbers' Paradox hasn't been superceded, the early physicists to consider the paradox, such as Halley and Cheseaux and, later, Olbers himself, tended to propose solutions of the (2b) type. They are sometimes unclear about what they intend, but their positions can often be associated with (2b1a) or (2b2a). Both of these positions create serious problems elsewhere in physics, the first with electrodynamics and the second with thermodynamics, for which no solutions were ever found. For instance, the amount of light hitting material obstruction in (2b2a) would result in a very, very hot universe. Cheseaux seems to have been the first person to consider seriously a solution of type (1), but Zollner is the first person to have actually argued for such a solution, preferring a (1b) solution in which the universe has finite mass in a finite Riemannian space. Working out solutions is not particularly easy sometimes, because not every proposed use of a limit on the parameters would really deal with the problem; if you proposed finite stars but allowed too many, you would still get a much brighter sky than we actually have, for instance.
The twentieth century introduces a few complications into the matter, with universe expansion and the greater need, arising from general relativity, to be careful with the precise meaning of the word 'finite' when talking about space and time, as well as analogies to other paradoxes (e.g., involving gravity). But the general shape of the paradox and its possible solutions is intact.
Olbers' Paradox is interesting in being a physical problem that potentially has indirect metaphysical implications. It provides a strong argument that the physical universe must have some kind of limit, whether in mass, or in space, or in time, or in the function of the laws of nature, that is itself in need of a more fundamental explanation. This is not itself a metaphysical point; but many forms of historical physicalism and naturalism explicitly attempted to deflate the claim that the physical universe itself needed an explanation by appealing to infinities in all of these matters. These forms of physicalism are less common than they used to be, but you still find popular forms, and they are still commonly encountered in science fiction (which may be one contributing factor in the fact that you can still find popular versions). These forms of physicalism assumed that such infinities could be posited cheaply; Olbers' Paradox establishes that they have costs, and even that some combinations of such infinities are inconsistent with the existence of the universe we know. Physicalists and naturalists cannot assume that they can offload explanatory questions about the physical universe onto infinity; they have to show that they can do so.
Various Links of Interest
* Jack Butler, Pagans, Gnostics, and Christians -- Oh My?, at "Religion & Liberty Online", reviews two recent books on shifts in religious culture.
I'm inclined to think that the categories of 'pagan' and 'gnostic' are probably not very useful in discussing our current culture -- as C. S. Lewis famously said, if only people were becoming pagans! -- and there's always a danger of exaggerating the degree of shift, or mis-assessing its permanence. People make a great deal about the 'rise of the Nones', but it is important to remember that we are coming off an all-time peak, post-WWII, in church attendance and explicit church membership; active churchgoers are still a much, much larger percentage of the overall population than they were at (say) the beginning of the nineteenth century, and social interactions like church attendance are already known to go through phases that are rather like boom-and-bust cycles. The fact of the matter is that we just don't really know what is going on or how long it will last, beyond the fact that there is some sort of major shake-up in the role of social institutions happening, of which churches just happen to be an especially prominent part, as they have overall so far collapsed from 'extremely and unusually successful social institutions' to 'only moderately successful social institutions'. This is not how these things are usually described, but it's much closer to how things are when descriptions are motivated by neither alarmism (if you regard it as a negative thing) or wishful thinking (for those who regard it as a positive thing).
* Andres Ayala, The Principle of Causality and the Notion of Participation: Deepening into Fabro's Defense of This Principle (PDF)
* Matthew Yglesias, Elite misinformation is an underrated problem, at "Slow Boring"
* Stewart Duncan, Cudworth as a Critic of Spinoza (PDF)
* Paul Schweigl, Fatty Bolger, a local hero, at "Front Porch Republic"
* Christopher James Masterman, What does nihilism tell us about modal logic? (PDF) -- this is a very interesting paper, and one that I'll have to consider at much greater length.
* Peter Salmon, Paper trails, at "Aeon", on the history of the archives of Husserl and Nietzsche.
* Amy Kind, Accuracy in imagining (PDF)
Currently Reading
Eric Nguyen, Things We Lost to the Water
Juan Donoso Cortes, Essays on Catholicism, Liberalism, and Socialism
John Matthews, The Great Book of King Arthur
On Audiobook
J. R. R. Tolkien, The Fellowship of the Ring (narrated by Rob Inglis)
Cixin Liu, The Three-Body Problem (narrated by Luke Daniels)
Frederick Douglass, My Bondage and My Freedom (narrated by Leon Nixon)
