# Bump: You know that obnoxious thing people do on the internet when they've said something and they feel they haven't been paid enough attention? I'm doing that.

Fragment of a discussion from User talk:Tmtoulouse

Define model, element in a model. Can you give a precise definition to these terms? I have some idea what you are talking about, but it would be clearer if you could define these terms more precisely.

Consider the following claim: "The universe will cease to exist on Friday 8th July 2011". How many "elements" are in that "model"? Considering the opposite claim: "The universe will continue to exist after Friday 8th July 2011". How many elements in the model of that claim? Is one of these statements more parsimonious than the other, or are they equal in complexity?

The relative time between now and that prediction is not a factor in the models complexity. So, its not the complexity of the universe that would exist were the model true, or the complexity of the observations we would expect to have were the model true, but the complexity of the model itself? This goes back to part of my point - we have multiple competing formulations of the principle of parsimony. Why choose to follow your formulation rather than some other one?

more complex models are better than simplier models when the residuals of the complex model are some significant value less than the simpler model. - comparing my two claims, i.e. the universe will suddenly end on this Friday, v.s. it will continue to exist after that date, how do their residuals differ?

08:35, 4 July 2011

A model is a set of causative or predictive rules/statements used to simulate some observed phenomenon.

An element of a model is a specific causative or predictive rule/statement with in the model's set.

A prediction is a specific predicted data point generated from the model to be compared with actual observation.

"The universe will cease to exist on Friday 8th July 2011" and "The universe will continue to exist after Friday 8th July 2011" are predictions not models.

A model would be something like: Since Gargurtle the giant turtle who exists outside of space and time and eats universes is coming for us next and will reach us on Friday 8th July 2011.

The elements of the model are: {All existing scientific theories}+the existence of Gargurtle

The prediction is: "The universe will cease to exist on Friday 8th July 2011"

The Gargurtle model adds an element to our model that adds zero explanatory power except for a single future prediction.

Until Friday 8th July 2011 the Gargurtle model has less epistemological value than the standard model.

18:19, 4 July 2011

Why should I adopt your "model theoretic" approach to the principle of parsimony? Why not another approach instead?

08:16, 5 July 2011

You don't have to do accept anything. The premise of this discussion is whether or not science as an epistemological framework has anything to say about the god hypothesis.

If you want to reject science and all that science tells us about reality that is your call. What you don't get to do is have your cake and eat it to, by claiming that you can accept science but reject what it would say about your made up god.

The approach to parsimony I have presented isn't "mine" its how science works. You can see it Bayesian model selection, or in something as basic as a statistical significance scale (hint why does the difference score increase for the same p-value as our degrees of freedom increase?).

Now this principle can be used for model-free approaches, but the same basic idea that predictive power has to scale up with degrees of freedom to maintain significance applies.

15:33, 5 July 2011

I have no problem with approaches which are genuinely part of science, as in required by and implied by science. But I can question whether the approach you've proposed is the only one which works with science. You claim science uses your interpretation of the principle of parsimony rather than some other - have evidence for that claim? You suggest that science only works with your interpretation of the principle of parsimony, and won't work with competing interpretations - have evidence for that claim?

I don't think science actually does use your principle of parsimony. Consider the theory of gravitation. Say we have Einstein's general relativity (hereafter GR), and we have some new theory, super-GR (maybe one of the GR alternatives listed by WP). Now, super-GR produces almost identical results to GR, except in very rare/extreme circumstances. Due to the rareity/extremity of those circumstances where super-GR behaves differently from GR, it is unlikely we will be able to distinguish super-GR from GR experimentally or observationally in the medium term. But, while Einstein's field equations are frequently lauded for their simplicity, super-GR's field equations are far more complicated. So, quite validly, physicists use the principle of parsimony to exclude super-GR: (1) GR and super-GR are experimentally/observationally indistinguishable at present; (2) GR is simpler than super-GR; (3) hence, prefer GR to super-GR. (Of course, maybe one day the experiments/observations needed to distinguish GR/super-GR will become feasible, and the results may actually favour super-GR. So, the rejection of super-GR by the principle of parsimony is provisional.)

Now, the reason I bring up this case, is that I think it demonstrates your account of the principle of parsimony - the "model element counting" approach you are using - doesn't match how scientists actually reason. GR and super-GR have the same elements in their model (spacetime, mass/energy, etc.). But super-GR's equations are much more complex than GR's. But I don't see how your model counting approach can measure the complexity of the equations, since all you do is count model elements. So, your definition of the principle of parsimony does not match the one actually used in science.

Moving on, let me produce two theories: theory 1: "The universe will instantaneously cease to exist this Friday". theory 2: "The universe will still exist this Saturday". Theory 2 is nothing more than the denial of theory 1. And what I've given is the whole of theory 1. There is no "Gargaturtle", no agent which ends the universe. The universe just ends for no particular reason. So these two theories have identical models. Hence, you can't use the principle of parsimony, as you describe it, to distinguish these two theories.

20:08, 5 July 2011

Ah, so that's what's happening on the 8th. I did wonder.

09:24, 5 July 2011