Naturalism

I've started reading the just-published book, God's Undertaker: Has Science Buried God?, of John Lennox, whom I met at St. Ebbe's. It's good. I think I see the essence of the philosophical position of Naturalism now,Click here to read more

from page 29:

[T]here is nothing but nature. It is a closed system of cause and effect. ...There is no `outside'.

The notion is tricky because naturalism does not, I think, exactly mean that magic and gods do not exist. There is no essential difference between a witch who mixes a love potion and a scientist who mixes a cough remedy except that the love potion doesn't work. Both mixers intend to repeat an objective formula to generate predictable results, and both have obtained their formula rationally, by accepting authority, using observation, or plausible theorizing. In the same way, whether we call the force that makes things pull at each other the force Gravity or the god Gravity makes no difference.

I would be hard put to say whether primitive peoples believe in naturalism or not. Their gods and demons are close to being explanations--- but on the other hand, they are believed to be fairly mysterious explanations. I suppose the key is whether the savages think that if they only had time, they'd be able to come up with a comprehensive explanation that included explaining the gods.

I was going to say that Thomas Aquinas thought he had such a comprehensive explanation (a summa theologica), but he didn't. He clearly distinguished between what could be known by reason and what needed to be learned by revelation, and he recognized that revelation did not include all the mysteries we'd like to know about God.

Thus, a naturalistic god is one that can be fully understood by humans-- at least understood as well as we understand, say, lions. He is a god that is in the same order of nature as man. The Greek gods of myth are like that, and the Norse gods, but lurking behind them is the truly supernatural--- the Mysteries, the Forms, the Norns, Erda.

Shoulder Muscles and Handwriting

"Tips for improving your handwriting," by Dyas A. Lawson sounds worth trying.Click here to read more

Here's it's idea for improving one's handwriting:

I’ve found only one reference to using the right muscle groups to write, and this is critical. I can’t be the only person who knows this; I’m neither that smart nor that good. Calligraphy instruction books address hand position, desk position, lighting, paper, you name it--but for some reason, not using the right muscles.

As you’ve probably surmised, the "right muscles" are not those in the fingers. You must use the shoulder-girdle and forearm muscles. This muscle group is capable of much more intricate action than you think and tires much less easily than fingers, besides giving a smooth, clean, sweeping look to the finished writing. Though it seems paradoxical, since we’re accustomed to thinking of small muscles having better control, the shoulder-girdle group, once trained, does the job better.

Weighted Least Squares and Why More Data is Better

<p>In doing statistics, when should we weight different observations differently?<p>

Suppose I have 10 independent observations of $x$ and I want to estimate the population mean, $\mu$. Why should I use the unweighted sample mean rather than weighting the first observation .91 and each of the rest by .01?<p>

Either way, I get an unbiased estimate, but the unweighted mean gives me lower variance of the estimator. If I use just observation 1 (a weight of 100% on it) then my estimator has the variance of the disturbance. If I use two observations, then a big positive disturbance on observation 1 might be cancelled out by a big negative on observation 2. Indeed, the worst case is that observation 2 also has a big positive disturbance, in which case I am no worse off by having it. I do not want to overweight any one observation, because I want mistakes to cancel out as evenly as possible.<p>

All this is completely free of the distribution of the disturbance term. It doesn't rely on the Central Limit Theorem, which says that as $n$ increases then the distribution of the estimator approaches the normal distribution (if I don't use too much weighting, at least!).<p>

If I knew that observation 1 had a smaller disturbance on average, then I *would* want to weight it more heavily. That's heteroskedasticity. <p>

Lizzie's Plus Table

Who Most Wants To Be Elected Policeman?

Jerusalem Post via National Review

 

Two weeks after Israel's alleged bombing raid in Syria, which some foreign reports said targeted North Korean nuclear material, the UN's nuclear watchdog elected Syria as deputy chairman of its General Conference on Monday.

Read more »

Asymptotics

Page 96 of David Cox’s 2006 Principles of Statistical Inference has a very nice one-sentence summary of asymptotic theory:

[A]pproximations are derived on the basis that the amount of information is large, errors of estimation are small, nonlinear relations are locally linear and a central limit effect operates to induce approximate normality of log likelihood derivatives.

Bayesian vs. Frequentist Statistical Theory

The Frequentist view of probability is that a coin with a 50% probability of heads will turn up heads 50% of the time.

The Bayesian view of probability is that a coin with a 50% probabilit of heads is one on which a knowledgeable risk-neutral observer would put a bet at even odds.

The Bayesian view is better.

When it comes to statistics, the essence of the Frequentist view is to ask whether the number of heads that shows up in one or more trials is probable given the null hypothesis that the true odds in any one toss are 50%.

When it comes to statistics, the essence of the Bayesian view is to estimate, given the number of number of heads that shows up in one or more trials and the observer’s prior belief about the odds, the probability that the odds are 50% versus the odds being some alternative number.

I like the frequentist view better. It’s neater not to have a prior involved.