One of my favorite places on the net to find really goofy bad math is Answers in Genesis. When I’m trying to avoid doing real work, I like to wander over there and look at the crazy stuff that people will actually take seriously in order to justify their religion.

In my latest swing by over there, I came across something which is a bizzare argument, but which is actually interesting mathematically. It’s an argument that the earth (or at least the milky way) must be at the center of the universe, because when we look at the redshifts of other objects in the universe, they appear to be quantized.

Here’s the short version of the argument, in their own words:

Over the last few decades, new evidence has surfaced that restores man to a central place in God’s universe. Astronomers have confirmed that numerical values of galaxy redshifts are ‘quantized’, tending to fall into distinct groups. According to Hubble’s law, redshifts are proportional to the distances of the galaxies from us. Then it would be the distances themselves that fall into groups. That would mean the galaxies tend to be grouped into (conceptual) spherical shells concentric around our home galaxy, the Milky Way. The shells turn out to be on the order of a million light years apart. The groups of redshifts would be distinct from each other only if our viewing location is less than a million light years from the centre. The odds for the Earth having such a unique position in the cosmos by accident are less than one in a trillion. Since big bang theorists presuppose the cosmos has naturalistic origins and cannot have a unique centre, they have sought other explanations, without notable success so far. Thus, redshift quantization is evidence (1) against the big bang theory, and (2) for a galactocentric cosmology, such as one by Robert Gentry or the one in my book, Starlight and Time.

This argument is actually an interesting combination of mathematical cluelessness and mathematical depth.

If you make the assumption that the universe is the inside of a giant sphere, expanding from a center point, then quantized redshift would be pretty surprising. Not just if you weren’t at the center of the universe – if the universe is an essentially flat shape, then a quantized redshift is very hard to explain. That’s because a quantized redshift in a “flat” universe would imply that things were expanding in a sequence of discrete shells, which would be quite a strange discovery.

But: if for some reason it was quantized, then no matter where you are, you will continue to see some degree of quantization in the motion of other objects. What you’d see is different redshifts – but they’d appear in a sort of stepped form: looking in any particular direction, you’d see a series of quantized shifts; looking in a different direction, you’d see a different series of shifts. The only place you’d get a perfectly uniform set of quantized shifts would be in the geometric center.

What the AiG guys ignore is the fact that in a flat geometry, the fact of quantized redshifts is incredibly hard to explain. Even if our galaxy were dead center in a uniform flat universe, the fact is, quantized redshifts – which imply discrete shells of matter in an expanding universe – are incredibly difficult to explain.

The flat geometry is a fundamental assumption of the AiG guys. If the universe is not flat, then the whole requirement for us to be at the center of things goes right out the window. For example, if our universe is the 3-dimensional surface of a four dimensional sphere – then if you see a quantized shift anywhere, you’ll see a quantized redshift everywhere. If fact, there are a lot of geometries that are much more likely to present a quantized redshift, and none of them except the flat one require any strange assumptions like “we’re in the dead center of the entire universe”. So do they make any argument to justify the assumption of a flat universe? No. Of course not. In fact, they just simply mock it:

They picture the galaxies like grains of dust all over the surface of the balloon. (No galaxies would be inside the balloon.) As the expansion proceeds, the rubber (representing the ‘fabric’ of space itself) stretches outward. This spreads the dust apart. From the viewpoint of each grain, the others move away from it, but no grain can claim to be the unique centre of the expansion. On the surface of the balloon, there is no centre. The true centre of the expansion would be in the air inside the balloon, which represents ‘hyperspace’, beyond the perception of creatures confined to the 3-D ‘surface’.

That’s the most substantive part of the section where they “address” the geometry of the universe. It’s not handled at all as an issue that needs to be seriously considered – but just as some ridiculously bizzare and impossible notion dreamed up by a bunch of eggheads looking for excuses to deny god. Even though it explains exactly what they’re trying to say can’t be explained.

But hey, let’s ignore that. Even if we do assume something ridiculous like a flat universe with us at the center, the quantized redshift is surprising. They specifically quote one of the discoverers of the quantization of redshift making this point; only they don’t understand what he’s saying:

‘The redshift has imprinted on it a pattern that appears to have its origin in microscopic quantum physics, yet it carries this imprint across cosmological boundaries.’ 39

Thus secular astronomers have avoided the simple explanation, most not even mentioning it as a possibility. Instead, they have grasped at a straw they would normally disdain, by invoking mysterious unknown physics. I suggest that they are avoiding the obvious because galactocentricity brings into question their deepest worldviews. This issue cuts right to the heart of the big bang theory–its naturalistic evolutionist presuppositions.

This is a really amazing miscomprehension here. They’re so desparate to discredit scientific explanation that they quote things that mean the dead opposite of what they say it means. They want it to say that the quantized redshift is unexplainable unless you believe that our galaxy is at the center of the universe. But that’s not what it says. What it says is: quantized shift is a surprising thing at all. It doesn’t matter where in the universe we are; if we’re in an absolute center (if there is such a thing), or if we’re on an edge, or if we’re in a random location in a geometry without an edge: it’s surprising.

But it is explainable by the very theories that they’re disdaining as they quote him; and in fact, his quote explains it. The best theory for the quantization of the redshift is that in the very earliest moments of the universe, quantum fluctations created a non-uniformity in the distribution of what became matter in the universe. As the universe expanded, that tiny quantum effect eventually ended up producing galaxies, galactic structures, and the quantized distribution of objects in the observable universe.

The quotation about the redshift pattern isn’t attempting to explain away some observation that suggests that we’re at the center of the universe. It’s trying to explain something far deeper than that. Whatever the shape of the universe, whatever our location in the universe, whether or not the phrase “the center of the universe” has any meaning at all, the quantized redshift is an amazing, surprising thing. And what’s particularly exciting about it is that this very large-scale phenomenon is a directly observable result of some of the smallest-scale phenomena in our universe.

Aside from that they engage in what I call obfuscatory mathematics. There are a bunch of equations scattered through the article. None of the equations are particularly enlightening; none of them actually add any real information to the article or strenghten their arguments in any way. They’re just there to add the gloss of credibility that you get from having equations in your article: “Oh, look, they must know what they’re talking about, they used math!”.