You recognize as a youngster that science, and music, and literature and writing—creative wonders—draw you along comfortable invisible force lines. But not opera. Overbearing, embarrassing falsetto vibrato is just wrong. As your joints grow creaky and more of your pate warms to the Sun, you know that this is a misperception. You stumble upon more of these, as you notice yourself more often assigning past vigorous feats of physical prowess to the unimportant pursuits of the unimportant young. You ponder these, your various misperceptions. And your misperceptions of misperceptions. Recursion tickles you.


You realize in the shower one day that your—and others’—universal cognitive foibles smacking into observable reality are an irresistible rabbit hole, wondrously vast and an endless source of material to contemplate. Like a particle in the three-body problem of celestial mechanics, your orbit is a tangled meandering, variously lured into the sphere of influence of first one and then the other of those two massive attractors, science and the creative urge. This resonates, and you realize a re-appreciation of past love.


Thus: what shall you write? Unuseful question. The world is big. Where shall you intend your aim? Better. Get thee to the shower!, your ever-reliable Delphic font of nearly every good idea.§ You love nature, and science—especially astronomy and math—and the scientific way of thinking, which come to you with joy and not pain. (This cannot be weird, surely—friends’ and society’s protestations notwithstanding.) The chasm awaits.


On a whim you schlep to a National Association of Science Writers conference, where you are isolated and small, sole introvert amidst a mind-bruising cacophony. Drilling through your crushing discomfort, you meet Roy Peter Clark’s Writing Tools: 50 Essential Strategies for Every Writer (you buy three copies), you hear Jonathan Coulton sing his wistful nerd anthem, “Code Monkey” (you buy three CDs), and a merciful soul tells you to read Lewis Thomas’s classic medley of essays, The Lives of a Cell: Notes of a Biology Watcher (why is there no Kindle version?). This is it. A trigger, an unlatching: your dormant writing compulsion awakens.

Astronomy with math. True stories, precisely told. A worthwhile target.


Halfway through college, you end the pleasant agony and decide astronomy over music. Seemingly by crazy random utterly naive inevitability, you become a professional astronomer. As your mop grows thinner and your knuckles grow larger, you realize the apparent randomicity is a misperception.

The equations, if you are wondering, tell how a massless particle moves in the combined gravitational fields of two massive objects in orbit about each other.¤ Think, for example, Sun–Jupiter–spacecraft. In astronomy, we call this the restricted three-body problem. It is astonishingly complex.

§ Perhaps only Death is a greater surety—though, surely, only by a little.

¤ For completeness:





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): 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)


Sense and Sensibility and the American Gun Culture

Sense and Sensibility.

Jane Austen put these two words together for a specific reason.

Sense: meaning, understanding, prudence, sound judgement.

Sensibility: sensitivity, awareness, empathy.

She didn’t have to worry about guns the way we do, the way America does today. But if she had I think she likely might have said something worth our while to contemplate. Sense. Sensibility.

We have yet another senseless shooting, this time too close to my home in Flagstaff. At Northern Arizona University, where a close family member teaches, a student retrieved a gun from his car and shot four students, murdering one. (One is still in the ICU.) Over a simple fist fight, hurt feelings, wounded pride — a child lies dead and many lives destroyed.

A spat quickly broke out online over whether or not to call this one (there are so very many) a “mass murder.” The NAU police reassured the public, saying that this was not like another mass shooting that had just happened at a college in Oregon. Others were not buying it. Perhaps because of the shock and cognitive dissonance that comes with a shooting that is too close, too personal, they are missing the point.

A common (sadly — shamefully — this is all too common) behavior can stem from a myriad of complex generators, complicated motivations, because human psychology is, in the now, a complex miasma of innate character, upbringing, experience, and happenstance — nature and nurture and randomness. Yet, dead people on the ground are dead people on the ground: mass shooting, mass murder.

What is the point?

Ask yourself: what is the most common denominator in each one of these mass shootings, this endless succession of mass murders, this underbelly of America’s prolonged spiral to suicide? The answer is readily apparent to anyone not blinkered by stubborn ignorance or mindless fear: the uniquely sick American obsession with weaponry, in concert with the rigidly immoral, ignorant, selfish, counterfactual, antifactual, infantile, long-bankrupt ideology of the right wing, one consequence of which — just one of innumerable repercussions from a depraved world view — is a near-complete absence of meaningful gun regulation.

To choose slaughter (intended or not) over minor inconvenience to the sensible — which is really what we are talking about with effective regulation of firearms — is not an act that comes from moral or ethical values; it is sick and depraved.

You may be thinking, “but this does not apply to me.” Do you choose to stand by and do nothing? Are you silent? Then you, too, have opted for preserving our awful status quo, for senseless bloodshed, shattered bodies, ruined lives, devastated families. Inaction is a choice.

Silence is a choice.

To choose instead reason, and sense, in light of overwhelming evidence; to proactively choose responsibility to the people around you, and empathy for those not in your shoes, and good governance in public policy — these come from ethical, moral values. Reasonable values. Wouldn’t this be better than continuing to tacitly approve senseless carnage?

That is the point.

It is time we start acting like adults, you and I — own up to our responsibility. It is up to you, and me, and you and you and you. The nature of this monster, this beast that we have allowed other monsters to create and nurture while you and I were distracted, is that none of us gets to opt out; you cannot not play.

So which do you choose? Continuance of our national blood bath? Or sense and sensibility?

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 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 have 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.