Previously, I mathematically modeled the impressiveness of a claim as a function of the extraordinariness of the claim. Basically, the more extraordinary a claim is, the less likely it is to be true, and thus the less impressive it is. However, an extraordinary claim with extraordinary evidence to support it can be very impressive indeed.
DeralterChemiker asked me an excellent question: where would I place a bunch of claims on the graph? Here I have a mathematical model, why don't I try applying it?
A. Big Bang Theory
B. String Theory
D. Life on Mars (microscopic)
E. Anthropogenic Global Warming
G. Orbital theory (ie gravity)
H. The existence of God (falls somewhere on the line depending on who's claiming it)
Of course, the whole thing is rather subjective, since there isn't any obvious way to quantify the extraordinariness and impressiveness of claims. Nor is it obvious how I should scale it (can gravity and homeopathy really be on the same graph without distorting the scale?). Really, it's the general method and general patterns which are important, not the conclusions.
However, I'd be interested to see some of my readers' conclusions. Where would you place some of the claims you've heard? For instance, Deralterchemiker also suggested plotting Obama's economic policy. But you can also try such favorites as "Brocolli is healthy" or "Human nature is essentially good". Give the coordinates: (extraordinariness of claim, amount of evidence)
When making this graph, it became clear to me that I needed to define terms. For my purposes here, the "extraordinariness" of a claim is basically a measure of how initially unlikely it is. A claim is extraordinary if it initially goes against common sense or common observations. A claim is extraordinary if it is very complex and specific, going against Occam's Razor. It is also extraordinary if it contradicts other well-established claims.
The other that became clear while making this graph, is that it's really difficult to judge where to place claims. I'm not happy with how the scaling turned out. And sometimes a claim is extraordinary precisely because it has evidence against it. How do you separate out extraordinariness and evidence anyways? I guess you gotta remember that "Extraordinary claims require extraordinary evidence" is simply a rule of thumb, not to be quantified unless you're feeling particularly artistic.