July 2008


In my paper “Design Inferences in an Infinite Universe”, I explore the status of design inferences under the assumption that the universe is spatially infinite. From a philosopher’s standpoint, this project has interest regardless of whether the universe is actually spatially infinite. But I do hold that whether the universe is spatially infinite can affect the strength of some design arguments for the existence of God, and hence, if one wants to know whether God actually exists in this universe, it could be relevant to establish whether the universe is spatially infinite. 

I didn’t try to establish that in my paper — to look at the evidence for and against the hypothesis that the universe is spatially infinite would take at least a whole paper, and would quickly get into some sophisticated physics. But I did provide two paragraphs of support for the hypothesis that the universe is spatially infinite, just to show that it is a live possibility amongst physicists. I got the following email in reply:

I have read your preprint with great interest. But,
allow me to say, you assume an infinite universe,
which is far from proven or accepted:

“The next question about the shape of the Universe is
to know whether space is finite or infinite –
equivalent to know whether space contains a finite or
an infinite amount of matter–energy, since the usual
assumption of homogeneity implies a uniform
distribution of matter and energy through space. From
a purely geometrical point of view, all positively
curved spaces are finite whatever their topology, but
the converse is not true : flat or negatively
curved spaces can have finite or infinite volumes,
depending on their degree of connectedness (Ellis,
1971 ; Lachièze-Rey & Luminet, 1995).”

Also,

“The new release of WMAP data (Spergel et al., 2006),
integrating two additional years of observation with
reduced uncertainty, strengthened the evidence for an
abnormally low quadrupole and other features which do
not match with the infinite flat space model (this
explains the unexpected delay in the delivery of this
second release, originally announced for February
2004).”

See:

http://xyz.lanl.gov/ftp/arxiv/papers/0704/0704.3374.pdf

I would be happy to see those alternatives integrated
in your excellent paper.

I mostly agree with this email (especially the part about my paper being excellent) — a flat space (i.e. a space with no global curvature) can have a finite volume, as a result of having a certain topology, and there is some evidence for connected topologies in the WMAP data. As far as I can tell, though, most physicists who pay attention to this sort of thing still think that the WMAP data is providing evidence for the hypothesis that the universe is spatially infinite. See, for example, this:

If the density just equals the critical density, the universe is flat, but still presumably infinite. The value of the critical density is very small: it corresponds to roughly 6 hydrogen atoms per cubic meter, an astonishingly good vacuum by terrestrial standards! One of the key scientific questions in cosmology today is: what is the average density of matter in our universe? While the answer is not yet known for certain, it appears to be tantalizingly close to the critical density.

Anyway, going back to the email, I’m surprised by the claim that the second release of WMAP data was unexpectedly delayed because it’s providing evidence for features that don’t match the infinite flat space model. This sounds like a strange sociological/conspiracy-theory type claim (I’m not sure exactly how to categorize it). I haven’t found anything definitive online, but I did find this:

Conspiracy theories abound on the delay in releasing WMAP year 2 results. The WMAP people are simply not talking, so take anything you see on the web with a healthy dose of salt. 

The fact that the author of that paper the email quotes from was willing to definitely state the reason that the data was delayed, with no support to back up that claim, makes me somewhat worried about the intellectual quality and the objectivity of the rest of the paper. 

Anyway the data are out now. They don’t seem to have anything especially definitively new to say about whether the universe is spatially infinite.

I support the passage of the Louisiana Science Education Act, which Governor Jindal recently signed. I recognize that this is not popular with fellow secularists. There’s a lot I could say about these issues (and I do say a lot in my forthcoming book). But for now here are a few blog-worthy thoughts.

In my opinion, what the act says is relatively innocuous:

The State Board of Elementary and Secondary Education, upon request of a city, parish, or other local public school board, shall allow and assist teachers, principals, and other school administrators to create and foster  an environment within public elementary and secondary schools that promotes critical thinking skills, logical analysis, and open and objective discussion of scientific theories being studied including, but not limited to, evolution, the origins of life, global warming, and human cloning. 

I am all for promoting critical thinking skills and logical analysis — this is what philosophers do, and I’ve encountered too many college students who are shockingly bad at it. As for open and objective discussion of scientific theories, I’m all for that too. Too often, science education consists of learning disconnected facts about the content of recieved scientific theories, facts which the students will forget soon enough anyways. Evidence suggests that students learn more when they are also taught how scientists reason, and how scientific inquiry happens. Having discussion about controversies in science will help students to see how scientists reason. 

What about focus on evolution, the origins of life, global warning, and human cloning — isn’t it clear that there’s some sort of political agenda there? First, I have to point out that that list actually doesn’t change the material content of the act; it just provides examples of the sorts of theories that could be talked about. But it’s clear that those theories are picked because they’re ones that are controversial in the public sphere in Louisiana. The fact that they’re controversial in the public sphere means that students are likely to have heard about them, and moreover, they’re likely to have heard some uninformed opinions about them. Without an act like the Science Education Act, teachers might feel compelled to side-step these controversial issues, and to avoid addressing the confused beliefs some students have, but with an act like this one, teachers can feel more emboldened to address the issues head-on. 

It’s clear that the worry from many secularists is that creationism or intelligent design will be taught as true in science class as a result of this act. Well, if that were to happen, teachers would be violating what the act says — they wouldn’t be having an open and objective discussion. But if that’s the worry, then the situation is no different than if the act hadn’t passed — we’d still have to worry about teachers violating the rules and teaching in a way that they’re not supposed to. But as long as teachers teach as they’re supposed to, then science students in Louisiana are better off as a result of this act being passed.

I received an email from someone wondering whether I knew about the Ikeda/Jeffreys paper on the fine-tuning argument, since I didn’t talk about it in my paper “God, Fine-Tuning, and the Problem of Old Evidence.” Here’s how I replied:

Yes, I am familiar with the Ikeda/Jeffreys paper. I’m not completely sure I get their argument, because to be honest the paper is a mess structurally (at least, the online paper is, and it doesn’t appear that they’ve published a cleaned-up version). But if I am understanding their argument right, then I would say that they are making the same mistake Sober makes, and they’re not taking into account that we sometimes legitimately change our probabilitiy assignments in light of old evidence. In the fine-tuning case, the fact that the universe exists with life is old evidence, but nevertheless proponents of the argument want us to change our probability assignments in part as as a result of that old evidence. Ikeda and Jeffreys don’t want to allow that:

Please remember that if You are a sentient observer, You must already know that L is true, even before You learn anything about F or P(F|N). Thus it is legitimate, appropriate, and indeed required, for You to elicit Your prior on N versus ~N conditioned on L and use that as Your starting point.

But I don’t see their argument for why one can’t treat L as old evidence, and reason probabilistically using L (and one of the standard solutions to the problem of old evidence, such as the ur-probability solution I give in my paper “God, Fine-Tuning, and the Problem of Old Evidence”). I can think of various prima facie plausible arguments that could be given for why one can’t treat L as old evidence, but I haven’t seen Ikeda/Jeffreys or Sober give even a prima facie plausible one. The argument that Sober does give forces him to say that in the firing squad example, where the person about to be shot at survives the shooting unharmed, that we observers can reason that his survival probably happened as a result of design, but he can’t. This is (in my opinion, at least) a clearly unacceptable result. That’s why I criticize it in my “God, Fine-Tuning, and the Problem of Old Evidence” paper, and Jonathan Weisberg also gives a good criticism of it in his BJPS paper “Firing Squads and Fine-Tuning: Sober on the Design Argument”.

On a different topic, I pretty much agree with the Ikeda/Jeffreys claim that an omnipotent creator could cause us to exist in any universe whatsoever, if the idea is that, even if the physical constants don’t have the right values to lead to a universe that’s friendly to standard embodied life, nevertheless God could put life in there, and ensure through occasionalist-style intervention that that life survives. This raises the point that there are two different theistic hypotheses one could consider — the hypothesis that God exists and God wants life, and the narrower hypothesis that God exists and God wants life existing in a universe in the standard sort of way that we’re familiar with. The fine-tuning proponent would say that the evidence we have supports both hypotheses (and presumably that it supports the second hypothesis more), but it could well be the case that the prior probability for the second hypothesis is lower than the prior probability for the first.

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