Flagstaff Skywheel 2015-11-07

distance to downtown (red line = 2.5 miles)
distance to downtown (red line = 2.5 miles)

Dark skies are a treasure, a part of our culture, a part of who we are as humans that we must preserve. Due to some enlightened and forward thinking in the late 1980s, the outdoor lighting code implemented in Flagstaff has thus far kept light pollution from completely overrunning our beautiful natural skies.

From my back yard, 2.5 miles from the downtown commercial business center (click the thumbnail at right), I can see stars as faint as about magnitude 5.5 on a clear, Moonless night. In the video, North is towards the upper left corner. On the left side (NE), you can see that the sky background is noticeably brighter than toward the SW at right. The center of downtown Flagstaff is toward the  NE.

This is 3.25 hours of the sky wheeling by in my Flagstaff back yard. Famous objects that appear: the Andromeda Galaxy (passes straight overhead), the Double Cluster in Perseus (left of Andromeda Galaxy), the Pleiades (towards the end, at the bottom), and Capella (towards the end, bright star at left).

Camera: Canon G3 X, 30 seconds per “video” frame (15-second exposures).

Panopticon Inverted

A 360-degree panorama from the U.S. Naval Observatory 61-inch telescope dome catwalk, stitched together from nine photos. (You’ll notice I caught the catwalk railing in one of the photos. Oops.) This was on 2015-11-06, with a Canon G3 X.

Probably the best way to view (and download) the full-resolution version of this 23,890×2,597 image, which has such an extreme aspect ratio, is to use the Google viewer (use the magnifier):  https://goo.gl/RTXJxp. The version below is 1/6 resolution. (After clicking to enlarge, right-click and open in a new tab to view the 1/6-resolution version.)

A catwalk panorama (click to enlarge)
A catwalk panorama (click to enlarge)

Zodiacal Light West of Flagstaff, Feb. 2015

U.S. Naval Observatory - Flagstaff Station (click to enlarge)
U.S. Naval Observatory – Flagstaff Station (click to enlarge)

The zodiacal light at 7:51 pm (MST) on February 10, 2015, as seen from the west parking lot of the U.S. Naval Observatory near Flagstaff. If you’re wondering where the Observatory is, it’s about five miles west of downtown (Google maps link).

Below are two versions of a stack of eight 30-second exposures taken with a ZWO ASI120MM camera mounted on a camera tripod. This was 1h 47m after sunset (6:04 pm), and 21 minutes after the end of astronomical twilight (7:30 pm). You can see several naked-eye astronomical wonders, which are marked on the annotated version:

Zodiacal light from NOFS, 2015-02-11 (click to enlarge)
Zodiacal light from NOFS, 2015-02-11 (click to enlarge)
Zodiacal light from NOFS, 2015-02-11, with annotations (click to enlarge)
Zodiacal light from NOFS, 2015-02-11, with annotations (click to enlarge)


Fun with Python

Draw your own conclusions:

Grammar vs. politics. Or, education vs. ideology.
Grammar vs. politics. Or, education vs. ideology. (click to embiggen)
The red points are data from a grammar.com analysis of nonnegative Facebook comments on the pages of these presidential candidates. The black curve is the most-optimal least-squares fit of a polynomial (fourth-order, in this case) that, among the polynomials tested (orders zero through eight), minimizes the information loss of that model representation of the data. This information loss minimization is called the Akaike Information Criterion.


Fast hairy monsters high up on a wall, incognizant of their fortune, being as they are — at least on occasion — and in more than one sense of the word, ascendant, beyond the ken of three prowling, ever-watchful, and even faster (as if that were imaginable, but imagination I’ve noticed often wears the Emperor’s illusory purple), hungry — or so they yowl at me, incessantly — feline beasts known throughout the land, their domain, not just for their sleek and deadly elegance but for torturing, and in turns dismembering, in that horrifying, playful, pure-sociopath way unique (one hopes) to their species — these nimble piliferous octopeds would be glad, if they but had the ganglions for it, that I spy them, at least some of them, first.

Is Trump’s Lead Significant?

Snapshot of polling results among Republican voters over the past three months [click to embiggen]
Snapshot of polling results among Republican voters over the past three months [click to embiggen]
At the moment, The Donald leads nationally among Republicans, with 29.8% favorability. Roughly 30% of polled Republicans currently favor Trump over the rest of the Republican Field of Clowns. People argue that 30 percent is not terribly impressive. Are they right?

You have to interpret more carefully than that. Roughly 30% of polled Republicans prefer Trump over the others. That last bit is important: that many other Clowns are vying for the prize matters in the interpretation of Trump’s 29.8 percent.

Since there are fifteen Clowns in this poll, an even distribution of favorability would be 6.7% per Clown. So Trump’s 29.8% is a pretty big outlier. How big? The mean of this favorability distribution is $\mu = 6.1$%, pretty close to the 6.7% expectation. The standard deviation of this distribution of Clown favorability ratings is $\sigma = 7.4$%. Trump’s $p = 29.8$% therefore is a $\Delta = \dfrac{\left|p\, – \mu\right|}{\sigma} = 3.2$-sigma outlier, which is statistically significant. What this means is that the chance of that being just a statistical fluke (i.e., the likelihood that a random choice from among a Gaussian distribution with $\mu = 6.1$% and $\sigma = 7.4$% would land you at 29.8% or higher) is $1 – \mathrm{erf} \left(\dfrac{\Delta}{\sqrt{2}}\right) = 0.0014 = 0.14$ percent.

In the physical sciences, a result lying three or more standard deviations away from the null hypothesis value is the typical bar for publishable significance. $\mathrm{erf}$ is the error function:

$$\mathrm{erf}(z) = \dfrac{1}{\sqrt{\pi}} \int_{-z}^z e^{-t^2} dt$$

and is the probability of a random variate lying between $-z$ and $+z$ in a distribution with zero mean and standard deviation $\frac 12$. Now, the 0.14% result above would hold if the favorability distribution were a normal (i.e., Gaussian) distribution, which it certainly is not. But the conclusions should correspond closely enough to reality to use as an approximate guide.

The next candidate down is Carson at 16.0%, and Bush is third at 8.3%. Carson is only 1.3 sigma out from the mean (Bush: $0.3\,\sigma$), which corresponds to the likelihood of his favorability rating being where it is or higher due to random chance is 18 percent (Bush: 77%).

Conclusion: Trump’s and Carson’s leads above the rest of this particular Republican Field of Clowns are currently significant, while for the rest it’s a coin toss in terms of preference — even for Bush.

Update 9/10: Numbers and graphic updated from original to reflect values current as of 10 September.