Friday, March 6, 2009

Extraordinary plotting

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
C. Evolution
D. Life on Mars (microscopic)
E. Anthropogenic Global Warming
F. Homeopathy
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.


DeralterChemiker said...

No one else has accepted your challenge to apply the graph to their opinions, but I will. I will use as coordinates (x,y,z) the coordinates (Extraordinary, Evidence, Impressive).

A. Big Bang Theory: (11,13,9) But I am not sure this fits on your surface, as you illustrated it. I feel that the evidence is not completely convincing for me, but how can anything be more extraordinary or more impressive than the cause for the existence of the universe?
B. String Theory: (3,1,1)
C. Evolution: (13,15,10)
D. Life on Mars (microscopic): (2,2,2)
E. Anthropogenic Global Warming: (4,7,4), or about where you put it.
F. Homeopathy: I pass on this. Homeopathy, as you describe it, has little or no evidence to support it. However, long ago when I was injured and our conventional doctor said he could not do anything for me, I took someone’s suggestion and went to a homeopathic doctor. His treatment, which consisted only of heat and rest, eased me through an extremely troubling time and allowed me to get on with my life. He did not cure me, of course. Years later, when the injury was aggravated again, conventional surgery had advanced to the point where it could give me much greater comfort, although it, too, could not heal me completely.
G. Orbital theory (ie gravity): (4,15,4), where you put it.
H. The existence of God: It depends on how you define God. If he is defined by the anthropological model of conventional religions as a being who interacts with us and is aware of our every thought and deed, I would place him at (15,-1,0). However, I would define God by the evidence, and for this I use the evidence of the Big Bang. If the Big Bang occurred, then it must have been brought about by an enormous creative force. If someone wishes to call this force the Creator, I can accept that; and if they wish to call that creative force by any other name (God, Yaweh, Allah), I can accept that. But I don’t know what that God is like, and I’m sure that no one else does. Therefore I call myself an agnostic deist. My coordinates for this type of God are the same as those for the Big Bang.
I. Obama's approach to solving the economic crisis: You did not respond to my attempt to draw you into an assessment of contemporary economic policy, which in many ways is more pertinent than the other issues for addressing the problems of the real world today. I would place it at about (4,14,5). I find that the evidence for the correctness of this approach is very strong, that it is not a particularly extraordinary approach, and therefore it is not a particularly impressive approach. If there were a fourth coordinate expressing my confidence in the approach, it would be very high (10 or more).

miller said...

Heh. I skipped the political one because I don't feel I have enough information to judge either way, pertinent though it may be.

Placing the deist god and the Big Bang Theory in the same location suggests that you think they are equivalent. I don't think Big Bang theory necessarily implies a deist god (and the creation of the universe isn't even included in the theory anyways). And I especially don't think that the deist god implies Big Bang theory, or anything at all. That's why I would place it at (0,0).

However, there are some claims, I think, which are impressive above and beyond what is in my model. For instance, evolution is pretty impressive because it's about the origin of us. Evolution has a lot of human interest. On the other hand, the theory of superconductors, while also rather extraordinary, might not excite as many people. It depends on who you are and what you like. So there's some level of subjectivity involved.