Towards a More Perfect Democracy

If you haven’t yet read Making Democracy Count: How Mathematics Improves Voting, Electoral Maps, and Representation by Ismar Volić (Princeton University Press, 2024) I strongly recommend that you do, especially if you live in the United States. It truly is an epiphany, one of the most important books I have ever read. And don’t let “mathematics” in the title scare you. The mathematics in this book is easy and straightforward, and greatly strengthens the validity of the recommendations presented. The book is organized so that a busy person can read just a few pages a day, with ample natural stopping points throughout its 340+ pages. The current edition is hardcover, and can be found for as little as $15. A paperback edition is due out in February.

The author, Ismar Volić, is Professor of Mathematics at Wellesley College and Director of the Institute for Mathematics and Democracy.

What follows here is a high-level introduction to some of the most important topics covered in the book. This is in no way a substitute for reading the book, however. Volić presents many alternatives, the pros and cons of each, and provides many examples, often from recent history. You need to read this book!

Majority vs. Plurality
A “majority” means that at least 50% of the voters select the winning candidate. A “plurality” means that whoever gets the most votes wins, no matter how small the percentage. Whenever there is an election with more than two candidates running, the winner often garners less than 50% of the vote in the plurality-based voting used in most U.S. elections. A candidate can win despite the majority having voting against them. This is inherently undemocratic. In this type of voting, we have no idea what a voter’s second choice would have been if their favored candidate does not win. Time and again plurality gives us minority rule.

Why on Earth should candidate A win with only 30% of the vote? This is undemocratic. (p. 30)

Plurality: More disadvantages

  • Extremely susceptible to external manipulation (e.g. the spoiler effect)
  • Extremely susceptible to strategic voting (e.g. tactical voting, insincere voting, dishonest voting)
  • Two-party systems benefit, effectively shutting out other political parties and independents

Ranked Choice Voting (Instant Runoff)
A voter is allowed (but not required) to rank two or more candidates so if their first choice is eliminated because that candidate had the fewest votes, their vote then goes to their second-choice candidate, and so on. This process of elimination of the candidate with the fewest votes continues until the winning candidate has received a majority of the votes.1

Supermajority vs. Simple Majority
In a two-candidate election, a simple majority (>50%) is the best voting method. A supermajority (some amount greater than a simple majority) is often arbitrary and unmathematical, and it’s inherently undemocratic.

What if you’re electing more than one candidate?
Ranked Choice Voting can be generalized if more than one candidate is to be elected. Here’s how it works. Depending only on the number of seats needing to be filled, a threshold percentage is determined. For all those who voted for the candidate with the most votes, only the fraction of your vote needed to meet the threshold is applied to that candidate, and the remainder of your vote goes to your second choice, and so on. For each voter, the fractions always add up to 100%. This method is called Single Transferable Vote.

Important Advantages to Ranked Choice Voting and Single Transferable Vote

  • Eliminates the “spoiler effect”. You can vote for who you like the best, regardless of their chances of winning, and your vote won’t inadvertently help to elect a candidate you don’t like.
  • Makes it possible to move away from our current two-party duopoly. Other political parties and independent candidates become viable, thus strengthening our democracy.
  • Greatly reduces negative campaigning
  • Greatly reduces political polarization
  • Increases voter turnout
  • Eliminates the needs for runoff elections and even primaries, reducing election administration costs and saving taxpayer dollars

Amartya Sen: 1998 Nobel Prize in Economics
Individual liberties are incompatible with social needs. A delicate balancing act is needed.

The U.S. House of Representatives

  • 435 seats is completely arbitrary
  • Until 1913, the size of the U.S. House of Representative has increased with population; since then, it has been frozen at 435 (except temporarily at 437 when Alaska and Hawaii became states)
  • A bigger House would go a long way toward correcting the multifaceted mess of the 1929 Reapportionment Act
  • Most of the world’s democracies have a lower chamber size that is close to the cube root of the population; if the U.S. followed that rule, we would have ~700 representatives instead of 435
  • Increasing the size of the U.S. House would stimulate greater political diversity and would help alleviate the effects of gerrymandering
  • Apportionment (determining how many House seats each state gets) uses a decent mathematical method known as Huntington-Hill; a slight improvement could be made if we used the Webster method of apportionment

Gerrymandering

  • Politicians choose the voters rather than the voters choosing the politicians
  • Independent, non-partisan commissions should determine federal and state congressional districts. After the 2020 census, only four states had independent commissions: Arizona, California, Colorado, and Michigan.
  • Increasing the size of the House of Representatives and consequently adding more districts and decreasing their size will decrease the ability to gerrymander them
  • Implementing multi-member districts with proportional representation and single transferable vote will eliminate gerrymandering once and for all; this will necessarily increase the size of the House and usually the size of the districts.

Multi-Member District Considerations

  • Works best if 3 to 5 representatives are elected for each district
  • If only 2 representatives for each district are elected, the entry bar is set too high (e.g. no effective challenge to the current two-party entrenched duopoly)

The Electoral College
Needs to be abolished. No other democracy in the world has anything like it. An amazing amount and variety of mathematical dysfunctions converge to make the Electoral College wholly unsuitable in a functioning democracy. The President needs to be chosen based solely on the national popular vote.

The Elephant in the Room: Campaign Finance Reform
Admittedly, campaign finance reform is beyond the scope of this book, mostly because mathematics has little to offer in support. It is entirely a political problem. Volić’s only comment about this occurs in a footnote on p. 40: “Citizen’s United reversed campaign finance restrictions, giving an upper hand to wealthy candidates.” In my opinion, Citizen’s United was one of the worst U.S. Supreme Court decisions in recent decades, and even calls into question the legitimacy of the Court. A top priority must be campaign finance reform if we are to have a properly functioning democracy. As it is, almost all candidates are bought and paid for by donors and special interests before they even take office. Ideally, all political campaigns should be publicly funded so no candidate has a financial advantage. Level the playing field so that the ideological merits of each candidate, their integrity, and record of public service is used to determine their worthiness, rather than how much propaganda their money can generate.

Concluding Thoughts
The democracy reforms needed in the United States are structural in nature. As the world’s oldest still-functioning democracy, the United States is beginning to show its age and is in need of a refresh. Many newer democracies have corrected some of our deficiencies and we could learn a thing or two from them. Thinking that we can effect substantive change only by continuing to feed the “two-headed monster” that is the Democratic and Republican parties is folly.

The ideas presented in this book need to become a regular part of our national conversation. Insist that political candidates publicly support at least once of these reforms, or refuse to vote for them. These reforms are inherently non-partisan. They will improve the quality of life of all citizens, regardless of their political party or persuasion. You can be sure that the most intense opposition to these ideas will come from those who currently hold an inordinate amount of power and wealth, and that don’t want to lose any of their current privileged status. But we vastly outnumber them. If we turn our collective ignorance to knowledge and apathy to action in sufficient numbers, we will succeed.

  1. In very rare cases, RCV instant runoff can result in a plurality rather than a majority election (the candidate wins with less than 50% of the vote). This can only happen when there are a large number of exhausted ballots (i.e. a significant number of voters do not rank candidates, or stop ranking them, say, after two candidates). Worst case scenario: everyone votes for just one person and does not specify a second choice when there are more than two candidates. ↩︎

Democracy Resources (not an exhaustive list!)

Fair Vote

Gerrymandering Project

Institute for Mathematics and Democracy

Our Common Purpose

Rank the Vote

Ranked Choice Voting Resource Center

Ranked Vote

RCV123.org

Transparent Election Initiative

Democracy Resources (Arizona)

Voter Choice Arizona

Arizona Independent Redistricting Commission

Block Your Neighbor’s Light

If you have a neighbor with a dusk-to-dawn insecurity light or a glare bomb that happens to be turned on while you’re engaged in astronomical pursuits, I have come up with a solution.

In the photo above, you will see a Uline 6 × 6′ Welding Screen Shade 8 (H-4610S8). The Shade 8 black vinyl tarp is almost opaque1 and does not have an objectionable odor, so you can store it in the house when not in use. I also ordered the optional set of four swivel casters from Uline (H-5388) so that the frame can easily be moved around by one person. One of these swivel casters is shown in the photo below.

I store the frame outdoors against the house under the patio roof. The canopy weight plates and frame’s minimal wind loading profile ensures that the frame will stay in place even in high winds. Once I roll the frame to the needed location to block the offending light, I use the canopy weight plates to keep the frame from moving while I am observing.

DSG Canopy Weight Plates from Dick’s Sporting Goods come as a set of four, and each one weighs 7.5 lbs. These keep the frame from moving during storage and when in use to block a neighbor’s light.

Since I wanted an easy way to hang the vinyl tarp on the frame and then remove it for storage inside after my observing session, I used four S-hooks from Ace Hardware. I used heavy-duty slip joint pliers to squeeze together the wide part of the S-hook that goes over the top of the frame so that it can’t come off of the frame. See the photo below.

To keep the S-hooks from sliding down off of the top of the frame, I made a couple of stops using Snake Wrap as shown in the photo below.

In addition to using the four S-hooks to hang the tarp, I also use a shoelace through the grommet nearest the top on each side to keep the tarp fully extended during light to moderate winds, as shown below.

In the final two photos, you see how the tarp moves as the wind blows against it. Allowing the lower part of the tarp to move when the wind blows reduces the wind loading on the light-blocking curtain.

  1. Only a tiny amount of light gets through the Uline Shade 8 black vinyl tarp (i.e. you can see where the light is on the other side of the tarp if you look right at it). If the light you are trying to block is extremely bright and you require a completely opaque tarp, if you can’t find a suitable 6 × 6′ tarp with at least four grommets on each side, I’d recommend purchasing a 5′ 6″ × 7′ 6″ Heavy Duty Reflective All-Purpose Weather-Resistant 9 mil Tarp from Harbor Freight. You’ll want to fold the long side at the bottom and hook the flap to the rest of the tarp using cable ties through the grommets so the length doesn’t exceed 6 ft. ↩︎

Vocabulary List

Here are a few interesting and perhaps useful words or definitions you may not know. Where a word has multiple meanings, only one (or some) of the meanings will be listed. I’ll be adding new words to this list from time to time. Definitions are taken from the Oxford English Dictionary and occasionally slightly modified for further clarity without changing the meaning.

ad hominem
Directed against a person rather than the position they are maintaining.
Latin: literally “to the person”

affable
Friendly, good-natured, or easy to talk to.

allegory
A story, poem, picture, music, etc. that can be interpreted to reveal a hidden meaning, typically a moral or political one.

anomie
Absence of the usual social or ethical standards of belief and conduct in an individual or group; (later also) a state of alienation from mainstream society characterized by feelings of hopelessness, loss of purpose, and isolation.

apocryphal
Of doubtful authenticity, although widely circulated as being true.

apologist
A person who offers an argument in defense of something controversial.

appellation
A designation, name, or title given to someone or something.

aptronym
A name regarded as (humorously) appropriate to a person’s profession or personal characteristics.

Arcadian
Ideally rural or rustic.
Arcadia is a mountainous district in the Peloponnese of southern Greece. In poetic fantasy it represents a pastoral paradise and in Greek mythology it is the home of Pan.

arcane
Understood by few; mysterious or secret.

augury
A sign of what will happen in the future; an omen.

auspicious
Conducive to success; favorable. Giving or being a sign of future success.

austere
1. Severe or strict in manner or attitude.
2. Having no comforts or luxuries.
3. Having a plain and unadorned appearance.
4. Of land, terrain, etc.: rugged, forbidding; harsh; bleak.

avuncular
Kind and friendly towards a younger or less experienced person.

bohemian
A person, especially one involved in the arts, who disregards or flouts social convention, and usually associates with others who have a similarly unorthodox lifestyle.

brooding
1. Engaged in or showing deep thought about something that makes one sad, angry, or worried.
2. Appearing darkly menacing.

cantabile
In a smooth flowing style, such as would be suited for singing.

capacious
Having a lot of space inside; roomy.

catharsis
The process of releasing, and thereby providing relief from, strong or repressed emotions.

coda
A concluding event, remark, or section.

collectivist
Relating to the practice or principle of giving a group priority over each individual in it.

complaisant
Willing to please others or to accept what they do or say without protest.
(Note: complaisant does not have the same meaning as complacent)

conflate
Combine (two or more sets of information, texts, ideas, etc.) into one.

contronym
A word with two opposite or contradictory meanings.
For example, sanction can mean both “a penalty for disobeying a law” and “official permission or approval for an action”.

cosseted
Cared for and protected in an overindulgent way; pampered.

declamation
A speech expressing strong feeling and addressed to the passions of the hearers.

deism
Belief in the existence of a supreme being, specifically of a creator who does not intervene in the universe.

demagogue
A political leader who seeks support by appealing to the desires and prejudices of ordinary people rather than by using rational argument.

diffident
Modest or shy because of a lack of self-confidence.

doctrinaire
Seeking to impose a doctrine in all circumstances without regard to practical considerations.

dolorous
Feeling or expressing great sorrow or distress.

doyen
The most respected or prominent person in a particular field.

effulgent
Shining forth brilliantly; sending forth intense light; resplendent, radiant.

élan
Energy, style, enthusiasm.

elegiac
Wistfully mournful.

entente
A friendly understanding or informal alliance between states or factions.

epistolary
Of or relating to letters or letter-writing.

eponymous
A person giving their name to something, or something named after a particular person or group.

equivocation
The use of ambiguous language to conceal the truth or to avoid committing oneself.

erudite
Having or showing great knowledge or learning.

esoteric
Intended for or likely to be understood by only a small number of people with a specialized knowledge or interest.

euphemism
A word or expression of comparatively favorable implication or less unpleasant associations substituted instead of a harsher or more offensive one that would be more accurate.

euphoric
Characterized by or feeling intense excitement and happiness.

ex nihilo
Out of nothing.

excoriate
To criticize someone severely.

exhortation
An address or communication emphatically urging someone to do something.

exiguous
Very small in size or amount; diminutive, minute; (also) very few in number, scanty, scarce.

existential
Involving or relating to the existence of a thing.

expropriation
The action by the state or an authority of taking property from its owner for public use or benefit.

fastidious
Very attentive to and concerned about accuracy and detail.

fervent
Of persons, their passions, dispositions, or actions: Ardent, intensely earnest; displaying a passionate intensity.

foil
A person or thing that contrasts with and so emphasizes and enhances the qualities of another.

furore
An outbreak of public anger or excitement.

guileless
Devoid of guile; innocent and without deception.

hagiography
A biography that treats its subject with undue reverence.

heuristic
Involving or enabling discovery or problem-solving through methods such as experimentation, evaluation, and trial and error.

histrionic, histrionics
1. Excessively theatrical or dramatic in character or style.
2. Melodramatic or hysterical behavior, typically intended to attract attention.

iconoclastic
Criticizing or attacking cherished beliefs or institutions.

idiom
1. The specific character or individuality of a language; the manner of expression considered natural to or distinctive of a language; a language’s distinctive phraseology.
2. A language, especially a person or people’s own language; the distinctive form of speech of a particular people or country.
3. In a narrower sense: a dialect or variety of a language; a form of a language limited to or distinctive of a particular area, category of people, period of time, or context.
4. A form of expression, grammatical construction, phrase, etc., used in a distinctive way in a particular language, dialect, or language variety; specifically, a group of words established by usage as having meaning not deducible from the meanings of the individual words.
5. A distinctive style or convention in music, art, architecture, writing, etc.; the characteristic mode of expression of a composer, artist, author, etc.

imperious
Arrogant and domineering.

inchoate
1. Just begun and so not fully formed or developed; rudimentary.
2. Confused or incoherent.

incunabula
1. The earliest stages of first traces in the development of anything.
2. An early printed book, especially one printed before 1501.
Singular: incunabulum

indolence
Avoidance of activity or exertion; laziness.

ineffable
That cannot be expressed or described in language; too great for words; transcending expression; unspeakable, unutterable, inexpressible.

ineluctable
Unable to be resisted or avoided; inescapable.

inexorable
1. Impossible to stop or prevent.
2. (of a person) Impossible to persuade; unrelenting.

innocuous
Not harmful or offensive.

innuendo
An allusive or oblique remark or hint, typically a suggestive or disparaging one.

insidiously
In a gradual, subtle way, but with harmful effects.

insolent
Showing a rude and arrogant lack of respect.

insouciant
Showing a casual lack of concern.

intelligentsia
Intellectuals or highly educated people as a group, especially when regarded as possessing culture and political influence.

intemperate
Characterized by or given to excessive indulgence in a passion or appetite.

invective
Insulting, abusive, or highly critical language.

itinerant
Traveling from place to place; a person who travels from place to place.

kakistocracy
Government by the least suitable or competent citizens of a state.

languor
1. Weariness of body, mind, or faculties; tiredness, fatigue; torpor, lethargy.
2. Drowsiness or inactivity, especially when pleasurable.
2. An oppressive stillness of the air.

leitmotif
A recurrent theme through a musical or literary composition, associated with a particular person, idea, or situation.

liminal
1. Occupying a position at, or on both sides of, a boundary or threshold.
2. Relating to a transitional or initial stage of a process.

longueur
A lengthy or tedious passage of writing, music, etc.; a tedious stretch of time.

luxuriate
Enjoy something as as a luxury; take self-indulgent delight in.

manqué
Having failed to become what one might have been.

mellifluous
1. Of speech, words, music, etc.: sweet, honeyed; pleasant-sounding, flowing, musical.
2. Of a speaker, writer, etc.: sweet-sounding; fluent; smoothly eloquent, charmingly persuasive.

memento
A reminder of a past event or condition, of an absent person, or of something that once existed; an object kept in memory of some person or event, a souvenir.

meritocracy
Government or the holding of power by people chosen on the basis of merit and competency (as opposed to wealth, social class, political party, ideology, etc.).

metonym
A word, name, or expression used as a substitute for something else with which it is closely associated.

milieu
1. An environment; surroundings, especially social surroundings.
2. A group of people with a shared cultural outlook.

mimesis
1. Imitative representation of the real world in art, music, literature, etc.
2. The deliberate imitation of the behavior of one group of people by another (usually less advantaged) as a factor in social change.

moot
1. Subject to debate, dispute, or uncertainty.
2. Having little or no practical relevance, typically because the subject is too uncertain to allow a decision.

nihilism
1. Total rejection of prevailing religious beliefs, moral principles, laws, etc., often from a sense of despair and the belief that life is devoid of any meaning.
2. More generally: negativity, destructiveness, hostility to accepted beliefs or established institutions.

orthodoxy
1. Belief in or agreement with doctrines, opinions, or practices currently held to be right or correct, especially in religious matters.
2. The body of opinions, doctrines, or beliefs held to be orthodox by a particular religion, society, or group.

pabulum or pablum
Bland intellectual fare, pap; an insipid or undemanding diet of words, entertainment, etc.

pantheism
A belief or philosophical theory that God identical with the universe; the doctrine that God is everything and everything is God. Frequently with implications of nature worship or love of nature.

pantheon
The group of people or things most revered by an individual, nation, profession, etc.; a group of people particularly respected, famous, or otherwise significant in some capacity; a set of things having acknowledged value or importance.

pareidolia
The perception of apparently significant patterns or recognizable images, especially faces, in random or accidental arrangements of shapes and lines.

part and parcel
1. An integral part of a larger whole.
2. Comprehensively; as an essential part; inextricably, inescapably.

patronizing
Apparently kind or helpful but betraying an attitude of superiority or condescension.

perfidious
Deceitful and untrustworthy.

pernicious
Having a harmful effect, especially in a gradual or subtle way.

peroration
The concluding part of a speech, typically intended to inspire enthusiasm in the audience.

perverse
1. Of a person, action, etc.: going against or disposed to go against what is reasonable, logical, expected, or required; contrary, fickle, irrational.
2. Contrary to what is morally right or good; wicked, evil, debased.
3. Contrary to an accepted standard or practice; incorrect, mistaken, wrong; (of an argument, interpretation, etc.) unjustifiable, contradictory, distorted.
4. Obstinate, stubborn, or persistent in what is unreasonable, foolish, or wrong; remaining set in a course of action in spite of the consequences.

philistine
A person who is hostile or indifferent to culture and the arts.

piquancy
The quality of being pleasantly stimulating or exciting.

polemical
Expressing or constituting a strongly critical attack on or controversial opinion about someone or something.

presentiment
An intuitive feeling about the future, especially one of foreboding.

prevarication
1. Deviation from a course thought to be right or proper; transgression of a law or code; an instance of this.
2. Departure from a rule, principle, or normal state; perversion or violation of a law, code of conduct, etc.; deviation from truth or correctness, error; an instance of this.
3. Divergence from a straight line or course.
4. Breach of duty or violation of trust in the exercise of an office; corrupt action, especially in a court of law.
5. Avoidance of straightforward statement of the truth; equivocation, evasiveness, misrepresentation; deceit; and instance of this.
6. Stalling or playing for time by means of evasion or indecisiveness; procrastination, hesitation.

probity
The quality of having strong moral principles; honesty and decency.

profligacy
Reckless extravagance or wastefulness in the use of resources.

prolepsis
1. The action of anticipating a possible objection or counter-argument in order to answer or discount it, or to deprive it of force.
2. A presupposition; something assumed to exist in advance.

propitious
Giving or indicating a good chance of success; favorable.

proselytize
1. Convert or attempt to convert someone from one religion, belief, or opinion to another.
2. Advocate or promote a belief or course of action.

protean
1. Adopting or existing in various shapes, variable in form; variously manifested or expressed; changing, unpredictable.
2. A person who or thing which changes form, character, nature, role, etc., rapidly or frequently.

provenance
1. The place of origin or earliest know history of something
2. The beginning of something’s existence; something’s origin.
3. A record of ownership of a work of art or an antique, used as a guide to authenticity or quality.

puerile
Childishly silly and immature.

pugnacious
Eager or quick to argue, quarrel, or fight.

pyrrhic
A victory won at too great a cost to have been worthwhile for the victor.

quaint
Attractively unusual or old-fashioned.

qualia
A quality of property as perceived or experienced by a person.

recapitulate
Summarize and state again the main points.

recension
A revised edition of a text.

recondite
1. Especially of a subject of study or discussion: little known or understood; abstruse, obscure; profound.
2. Of a writer: using abstruse or obscure allusions or references.
3. Of a thing: removed or hidden from view; kept out of sight.

redolent
Strongly reminiscent of suggestive of.

reductionism
The practice of analyzing and describing a complex phenomenon in terms of its simple or fundamental constituents, especially when this is said to provide a sufficient explanation.

restive
Unable to remain still, silent, or submissive, especially because of boredom or dissatisfaction.

salient
Most noticeable or important; prominent; conspicuous

scion
A descendant, especially one belonging to a wealthy or noble family; an heir.

sobriquet
A person’s nickname.

solicitous
1. Characterized by or showing interest or concern.
2. Eager or anxious to do something.

somnambulant
Resembling or characteristic of a sleepwalker; sluggish.

sophistry
1. The use of clever but false arguments, especially with the intention of deceiving.
2. A fallacious argument.

straw man
1. An intentionally misrepresented proposition that is set up because it is easier to defeat than an opponent’s real argument.
2. A person regarded as having no substance or integrity.

supine
Failing to act or protest as a result of moral weakness or indolence.

sycophant
A person who acts with ready compliance or eagerness to serve or please towards someone important or having power in order to gain personal advantage.

tautology
The saying of the same thing twice in the same sentence using different words, generally considered to be a fault of style; a phrase or expression in which the same thing is said twice in different words.

teleological
Relating to or involving the explanation of phenomena in terms of the purpose they serve rather than of the cause by which they arise.

tetchy
Irritable and bad-tempered.

trenchant
Vigorous or incisive in expression or style.

tripe
Nonsense; rubbish.

triptych
A set of three associated artistic, literary, or musical works intended to be appreciated together.

truculent
Quick to argue or oppose; aggressively defiant.

tyro
A beginner or novice.

Umwelt
The world as it is experienced by a particular organism.

unassuming
Not pretentious or arrogant; modest.

universalist
A person advocating loyalty to and concern for others without regard to national or other allegiances.

unpretentious
Not attempting to impress others with an appearance of greater importance, talent, or culture than is actually possessed.

vapid
Offering nothing that is stimulating or challenging; bland

verboten
Forbidden; not allowed.

viridescent
Greenish or becoming green.

wheedling
Using flattery or coaxing in order to persuade someone to do something or give one something.

USGS Astrogeology: Gazetteer of Planetary Nomenclature

We humans love to name things, and that extends to the heavens as well. The International Astronomical Union (IAU) has a working group and several task groups whose responsibility it is to approve the official names of topographic features of the planets, satellites, and minor objects in our solar system. Current members are listed here:

IAU Working Group and Task Group Members

You’ll find more information, search functionality, and alphabetical (alpha-beta-ical) lists of features at https://planetarynames.wr.usgs.gov/.

Incidentally, you might notice that many craters on Mercury are named after composers. Since many of the craters on the Moon are named after scientists, in fairness it was decided that many of the craters of Mercury (ostensibly similar to the Moon) should be named after composers, artists, writers, and others who have contributed to the arts and humanities. So there you have it!

A Tucson Symphony Suggestion

If the Tucson Symphony published a list of every piece they have ever played, I can guarantee you that I could provide them with a list of dozens of great orchestral works from past and present times that they have never played that I am certain would be well received by the listening public. And I am sure there are other TSO season subscribers who could also make such a list of never-before-programmed yet accessible works. My point is—and this would apply to any symphony orchestra—that some of us classical music lovers have devoted a lot of time and energy uncovering great music that is not part of the standard repertoire. Yes, we do love the standard repertoire as much as anyone, but wouldn’t it be exciting to regularly hear great orchestral works that our beloved orchestra has never played before?

Composer and musicologist Robert Greenberg speaks frankly and convincingly about this and related subjects at the end of the last episode of his 2011 DVD lecture series The 30 Greatest Orchestral Works1:

What Will Happen to the Orchestra?

Any institution that relies strictly on the past to preserve its future is dead meat. America’s orchestras do not perform nearly enough contemporary music and are therefore failing to create that very repertoire that will guarantee their relevance into the future. Assuming that I am right about this, and I most certainly am, we must then ask whose fault is this? The answer, sadly, is the obvious one. It’s our fault. It’s the audience’s fault.

Orchestras are market-driven institutions that are struggling to stay alive. The margin between breaking even and bankruptcy-inducing debt can be the ticket sales for just a few concerts. For the most part, modern audiences go to concerts to be entertained by music that is familiar, a fact that militates entirely against the creation of new repertoire. I, for example, would love to compose for orchestra, but I will not waste my precious time writing music that will never be played or that will only be performed once. This is a sentiment shared by virtually every one of my colleagues whose creative energies are being lavished instead on chamber music and vocal music.

By my unofficial count, there are 223 professional orchestras in the United States and Puerto Rico, most of them regional orchestras. In a world in which the basic repertoire has been recorded a thousand times over at a time when more and more people are forgoing the comradery of the concert hall in favor of consuming their music in their cars and in front of their computer screens, the great bulk of those 223 orchestras will simply become irrelevant in a generation unless they do something to make themselves relevant. Taking music to the schools certainly helps as does giving performances in unusual venues. But, really, it is music that feeds the orchestral beast, and without the roughage provided by fresh music, the beast will die of unrelieved constipation.

Cultivating and performing new orchestral music is not an aspect of an orchestra’s mission or even a duty. No. Along with playing the pre-existing repertoire, cultivating and performing new music is the orchestra’s very reason to be. Just as living things mate and reproduce in order to guarantee the survival of their genetic lines, so the orchestra as an institution must create viable repertoire in order to stay relevant and therefore to survive. In this, orchestras must lead and not be led by polls that ask their audiences what music they should perform. There should be a piece of new music five to eight minutes long on every concert program, with a longer featured new work appearing, say, two or three times a season.

When it comes to new music, charity starts at home. Local composers should be cultivated, commissioned, and then paraded on stage before the performance so that (1) the audience can see that they are indeed alive, and (2) so that the the composers might briefly describe what their pieces are about. Conductors must become, as they once were, advocates for fresh repertoire. The orchestral players, realizing that their careers are at stake, must forgo their usual cynicism and lassitude over having to learn a new piece and actually practice their parts at home so that the brief amount of rehearsal time allotted to the new work can be used effectively. The performances of these new works should be posted on an orchestra’s website so that anyone, anywhere can hear what is fresh and new and exciting, in Texarkana, or Sarasota, or Hartford, or Oakland.

Regional orchestras should band together to create consortia that would commission emerging and mid-career composers of promise to compose works, particularly concertos that would feature the section leaders of the orchestras themselves. Yes, charity starts at home. Why bring in an overpriced outsider when your own principal flutist, for example, would be thrilled to be a featured soloist.

The composers themselves also have a huge responsibility as well. I would suggest that they take a page from Aaron Copland’s compositional career. Copland’s chamber music tends to be quite virtuosic and uncompromising in its modernity, while his orchestral music, which he knew he was writing for a wider public, tends to be relatively less virtuosic and more accessible. Now, Copland wasn’t writing down to his orchestral audiences. No. He was writing smart on exactly these lines and in direct opposition to the modernist screed, “Who cares if you listen?” Contemporary composers must care who listens. And if we want the traditional orchestral audience to re-embrace what is new, we as composers have to be willing to meet the audience halfway by composing music that gives something back immediately in terms of rhythm, melody, harmony, and expressive content. In all fairness to most living composers, I would point out that the daunting and ferociously modernistic music of the post-World War II era, music that gave the phrase “modern music” a bad name, has been pretty much a thing of the past since the 1980s. Generally, but accurately speaking, most contemporary composers would no more write such ear-scalding music than drink battery acid.

The local media, radio, and press must commit themselves to new programming as well, with the knowledge that by doing so they, too, will be making themselves culturally relevant. A sense of importance and occasion could be built around the performances of even short pieces of new music that could begin to transform an orchestra’s self and public image.

Speaking of the public, it is all too easy to be cynical about public taste. From David Hannum’s famous line, misattributed to P.T. Barnum, that there’s a sucker born every minute, to H.L. Mencken’s admonition to never overestimate the intelligence of the American people, we are faced daily with the evidence of our cultural cretinism, from network television to Chia Pets, but I would point out that a concert hall is not a baseball stadium and that filling the seats of a concert hall is not a matter of drawing 45,000 people but rather of attracting those people who are predisposed, or who could be made to be predisposed, towards concert music in the first place. I am just foolish enough to believe that if you give the music-liking public a reason to believe there’s something new and exciting happening at the concert hall that they can’t get and won’t find anywhere else, they might very well show up!

We can only hope that at least some of this comes to pass because I fear that the epitaph, particularly for regional orchestras, is already being written. “Here lies an organizational dinosaur that never figured out how to maintain its duty to the past while staying relevant to the present.” Let us hope that such reports of the orchestra’s possible demise are entirely premature.

I would like to offer a few comments on Greenberg’s enlightening essay.

The Tucson Symphony, like many orchestras I’m sure, frequently presents new and often commissioned works, though they are always short, no more than 10 or 15 minutes in length. Many of these works are pleasant enough to listen to, but where are the more substantial works? The new symphonies and the new concertos? Also, there is an overemphasis on works from the Americas. In my opinion, most of these works are heavy on percussion and light on melody, harmony, and thematic development. I find what is going on in Europe, especially Eastern Europe, to be much more interesting and substantial. I would like to see some of these contemporary European works played. And there are many, many works from the past from all over the world that are not in the standard repertoire that also deserve to be regularly heard.

Greenberg brings up a disquieting thought: that composers won’t write what won’t get played. In other words, it may be that the reason we don’t have more symphonies, tone poems, suites, and concertos being written today is that the public isn’t demanding and, yes, paying for them. We could all be doing more to encourage composers to write longer and more substantial orchestral works and to see that they get performed by many orchestras and, yes, commercially recorded and released on CD. I do think this is more of a problem in the United States than it is in Europe, however.

In conclusion—and to expand on my original suggestion for the TSO—are there any orchestras that provide a complete list of all the works they have ever played on their website, and that invite suggestions for works not on this list from their concertgoers, and that program some of them? How exciting that would be!

  1. Greenberg, Robert. 2011. The 30 Greatest Orchestral Works. The Great Courses. ↩︎

Cecilia Payne and Gustav Holst

Cecilia Payne-Gaposchkin (1900-1979), as a woman, had to endure an enormous number of challenges and setbacks but her perseverance, professional dedication, and brilliance led her to become one of the important astrophysicists in the 20th century. In her 1925 Ph.D. thesis, Cecilia Payne demonstrated that stars are primarily composed of hydrogen and helium. This was highly controversial at the time, but she was eventually proved correct. In 1960, the noted astronomer Otto Struve called her 1925 thesis, Stellar Atmospheres; A Contribution to the Observational Study of High Temperature in the Reversing Layers of Stars “the most brilliant Ph.D. thesis ever written in astronomy.” Cecilia Payne-Gaposchkin would make an excellent subject for a full-length documentary as well as a biographical movie, and it is disgraceful that neither has been done yet.

I recently completed teaching a new five-week course on the English composer Gustav Holst (1874-1934). The research I did for that course plus my lifelong interest in astrophysics naturally led me to take an interest in the relationship between Cecilia Payne and Gustav Holst. Clearly from what you will see below, they had profound respect and admiration for each other.

Cecilia Payne attended St. Paul’ Girls’ School, where Gustav Holst taught, during the 1918-1919 school year. However, Holst left for war service in Salonika, Greece on October 29, 1918 and didn’t return to St. Paul’s until the 1919-1920 school year, after Payne had graduated and gone on to the University of Cambridge in Cambridge, England.

Frances Ralph Gray was the founding “high mistress” of St. Paul’s School for Girls in the Brook Green neighborhood of London…Like Cecilia, she adored music; unlike Cecilia, she had had great difficulty learning mathematics. Also unlike Cecilia, she was small in stature. She was, however, commanding in presence. Students reported that being sent to see Miss Gray “was their greatest fear.”

Frances perceived that there was something different about the seventeen-year-old girl in her office who so wanted to be admitted. Yes, Cecilia had been told to leave her current school, but not because she was disruptive or a problem learner—quite the opposite. She was a serious student who loved music and science, whose goal was to go to Cambridge. She had responded to Elizabeth Edwards and to Dorothy Daglish. If St. Paul’s had similar teachers who could recognize Cecilia’s love of learning and would take time to nurture her, surely she would be a good fit.

Years later, in a touching letter recommending Cecilia for a fellowship at Harvard, Frances wrote: “It is not my practice to admit girls who have reached the age at which Cecilia Payne was admitted [age seventeen], but I was requested to make an exception in her case by the headmistress of the School she had previously attended, who assured me that she was a girl of very unusual promise.”

Unbeknownst to Cecilia, St. Paul’s needed her as much as she needed the school. Founded just over a decade earlier by the Worshipful Company of Mercers, it prided itself on consistently outperforming other schools. The “Paulinas” were not viewed as, or trained to be, socialites; this was a serious school. The social snobbery of other private schools had no place here.

Cecilia described her move to St. Paul’s as stepping from medieval times into the modern day. Instead of chapels there were laboratories—in biology, chemistry, physics—and teachers who were specialists. Here she was not just “allowed” to study science; she was encouraged. She only attended the school for one year. But from the moment she approached the Queen Anne-style pink brick building and walked up the stone steps and through the marble and oak arched front door, she was home.1

Donovan Moore goes on now to write about Holst.

Frances Gray…made good on her professed love of music when she hired Gustav Holst. Holst was a relatively unknown trombone player when he accepted the job of director of music at St. Paul’s. Like Cecilia, he was shy and reserved, and he disdained fame. And like Cecilia, he was practiced in overcoming obstacles: neuritis in his right arm had forced him to stop playing the trombone and the piano, so he had to turn to composing.

Frances encouraged him; in fact, she worked with him, supplying the text for both a light-hearted masked dance in 1909 and a more ambitious orchestra work three years later. She had an entire music wing built in 1913, including a large soundproof room where Gustav composed on Sundays, when the school was locked up, in silence and solitude. It was in this room that he wrote his most famous work, the orchestra suite The Planets. Cecilia was among a group of students who heard it performed shortly after it was composed.2

As we shall see later through Cecilia’s own words, she must have heard some sort of run-through of The Planets at St. Paul’s. I wonder whether she was among the invited audience of about 250 people who attended the first performance of The Planets at Queen’s Hall, London, on Sunday, September 29, 1918, with Adrian Boult conducting the New Queen’s Hall Orchestra? Given that the choir for “Neptune: The Mystic” in that performance was comprised, in whole or in part, of students from St. Paul’s, it is possible she was present for the Queen’s Hall performance though perhaps unlikely given that the audience consisted of close friends and associates of Holst and many professional musicians in London.

Holst was also a great teacher. For three decades—from 1905 until his death in 1934—”Gussie”, as he was known, would cast his musical spell over his students. The contemporary composer Ralph Vaughan Williams described Holst’s long tenure at St. Paul’s: “He did away with the childish sentimentality that schoolgirls were supposed to appreciate and substituted Bach and Vittoria; a splendid background for immature minds.”

Holst discerned Cecilia’s love of music. He asked her to play her violin for him, made her a member of the school’s orchestra, and taught her how to conduct. He encouraged her to become a musician but did not prevail. Cecilia instinctively felt that a career in music would control her; as a scientist, she would be in control.3

In her autobiography, Cecilia Payne-Gaposchkin writes of St. Paul’s, Holst, and music:

The school ministered to my twin loves, science and music. Here I came under the spell of Gustav Holst, or “Gussie” as we affectionately called him. Aside from my shadowy Father, and my schoolboy brother, he was the first man I ever knew. He radiated music; the organ in the great hall reverberated to the great Toccata and fugue of Bach. Here for the first time I heard The Planets (then newly composed) and took part in a performance of the Hymn of Jesus. He was like a father to us, shy, abrupt and charming. He was quick to learn of my love of music, asked me to play the violin to him, and urged me to become a musician. I played in the orchestra, and learned conducting from him, but my love of science triumphed. It seems odd to think that the only career I was ever encouraged to follow was that of a musician. As a student at Cambridge I trained and conducted a choir that won an award. One of the judges told me that my conducting had been the decisive factor, and that my future lay there. Indeed, the feelings evoked by conducting a choir or orchestra are so powerful as to be overwhelming, but I recoiled instinctively from something I felt would control me; as a scientist I should be in control of my material. Who knows whether I was right?4

St. Paul’s Girls’ School did indeed have a great hall with an organ, so one wonders how Cecilia Payne heard The Planets there. It is also interesting that she first heard The Hymn of Jesus at St. Paul’s during her 1918-1919 school year, as the first known performance was on March 10, 1920 at the Royal College of Music with Holst conducting. Though Holst began composing the work during the summer of 1917, it was apparently not completed until after he returned from war service in Salonika, Greece on June 29, 1919. Cecilia Payne must have heard an early version of the work, or a part of it that had been completed.

Following four years at the University of Cambridge, Cecilia Payne arrived in New York aboard the RMS Laconia on Thursday, September 20, 1923, and from there proceeded to Cambridge, Massachusetts to begin her work in astronomy at Harvard University. Just a few months earlier, Gustav & Isobel Holst had visited the United States from April 27 through June 12, 1923. This was Isobel Holst’s only visit to the U.S., but Gustav would make two more visits, in 1929 and again in 1932.

Gustav Holst was in the United States from April 16-27, 1929, and on the evening of Friday, April 26, 1929, Holst gave a well-received lecture at Harvard University. It seems likely that Cecilia Payne would have attended that lecture and visited with Holst, but he was only in Cambridge for a day and had to take an early morning train to New York to board the RMS Samaria for the trip back to England. I have not been able to find any evidence that indicates they saw each other during Holst’s 1929 American visit.

Nor have I found any evidence that Cecilia Payne visited Holst in England after she moved to the United States in 1923, though New York ship passenger records show she arrived in New York from Southampton, England aboard the SS Leviathan on September 21, 1925, aboard the SS Berengaria on January 3, 1929, and aboard the SS Bremen on October 7, 1931 and August 30, 1933.

Gustav Holst and Cecilia Payne did meet again in 1932, when Holst conducted the Boston Symphony Orchestra at the first of two concerts in Symphony Hall in Boston.

After the concert Holst met Mrs. Arthur Foote and Cecilia Payne, a St. Paul’s Girls’ School alumna, who was studying astronomy.5

This would have been Friday, January 22, 1932, during Holst’s final visit to America. The all-Holst concert was at 2:30 p.m. and featured St. Paul’s Suite; Prelude and Scherzo, “Hammersmith” (Boston premiere); and the Ballet from the Opera, The Perfect Fool (Boston premiere); followed by an intermission and then The Planets. Here is the concert program courtesy of the Internet Archive which includes pages from the previous program suggesting that a last-minute program change occurred substituting St. Paul’s Suite for Somerset Rhapsody (an excellent early work by Holst, by the way) and switching the order of Hammersmith and The Perfect Fool:

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Incidentally, you might notice from the program that Arthur Fiedler was a violist in the orchestra and prepared the women’s chorus for the final movement of The Planets.

I met one ex Paulina at Harvard—Cecilia Payne who is doing research in astronomy.6

This is from a letter that Holst began on Tuesday, January 26, 1932 to his daughter Imogen.

He also spent some time with ex-Paulina Cecilia Payne, meeting her for lunch one day and for dinner at her place on another. This was followed by her lecture on a subject of great interest to him, the Zodiac.7

This was after Holst returned to Harvard from his four-day trip to Montreal and New York, and before his lecture at the Library of Congress in Washington, D.C., thus sometime between Tuesday, March 15 and Saturday, March 26, 1932.

Holst’s train from Ann Arbor arrived at Boston’s South Station at 11:15 a.m. on Saturday, May 21st. The next two days were spent packing and writing letters. He met with the Davisons the following morning and had dinner with Cecilia Payne at the Faculty Club that same evening.8

This dinner with Cecilia Payne would have been the evening of Sunday, May 22, 1932.

Later that same evening, Cecilia Payne drove Holst over to the observatory to view Jupiter and a star cluster. Holst enjoyed her company and visited with her again the day of his Boston departure.9

The observatory visit would have been on Tuesday, May 24. I’m guessing that the star cluster they observed after Jupiter would have been M13 in Hercules, which that evening was high in the eastern sky. Holst’s last visit with Cecilia Payne was on Thursday, May 26, 1932. Later that day, he left Boston by boat for New York where he boarded the SS Europa the following day to return to England. This was the last time Holst and Payne saw each other.

Cecilia Payne first met Russian-born astrophysicist Sergei Gaposchkin at the Astronomische Gesellschaft (Astronomical Society) meeting in Göttingen, Germany, on August 4, 1933. She helped him emigrate to the United States, and they were married on March 5, 1934. Less than three months later, Gustav Holst would be dead.

  1. Moore, Donovan. 2020. What Stars Are Made of: The Life of Cecilia Payne-Gaposchkin. London, England: Harvard University Press, pp. 34-35. ↩︎
  2. Moore, pp. 37-38. ↩︎
  3. Moore, p. 38. ↩︎
  4. Haramundanis, Katherine. 1984. Cecilia Payne-Gaposchkin: An Autobiography and Other Recollections. Cambridge, England: Cambridge University Press, p. 108. ↩︎
  5. Mitchell, Jon C. 2001. A Comprehensive Biography of Composer Gustav Holst, with Correspondence and Diary Excerpts: Including His American Years. New York, NY: Edwin Mellen Press, p. 442. ↩︎
  6. Mitchell, p. 447. ↩︎
  7. Mitchell, p. 485. ↩︎
  8. Mitchell, p. 543. ↩︎
  9. Mitchell, p. 547. ↩︎

Tucson Needs Evening and Weekend Classes

Since 2023, I’ve been teaching in-person classical composer music courses in Tucson. I’ve had to do all the work myself (preparation, venue, recruitment, publicity, etc.) because none of the existing continuing education organizations in the Tucson metro area offer evening and weekend classes. Moreover, the primary organization providing continuing education courses in Greater Tucson, Osher Lifelong Learning Institute—University of Arizona (OLLI-UA) adds the additional restriction that their advertised target audience includes no one under the age of 50. Since my music courses are expressly intended for anyone interested in learning more about classical music, high-school age and older, I have had to set about on my own with no organizational support whatsoever. It has not been easy.

Anyone who has attended a symphony or chamber music concert over the last few years will notice that audiences are generally dwindling and the vast majority that do attend these concerts are folks in their 60s, 70s, or older. In my own small but determined way, I am attempting to help reverse these trends by helping folks—especially younger folks—to see that classical music can be as exciting, meaningful, and inspirational as the best of whatever other kinds of music they’ve been listening to—even more so. I am teaching the kind of music classes that I wish someone had taught me when I was a young adult. Since my interest and expertise is in building audiences for classical music, both live performances and recorded music (because, let’s face it, there is a lot of great music that most of us will never have the opportunity to hear in live performance, no matter where we live), I focus mostly on listening enjoyment and the “life and times” of each composer rather than on music theory. Even though my courses are entitled Music for Listeners, I have no doubt that professional and amateur musicians will also enjoy the meticulously-researched “deep dive” into the life and music of each composer while at the same time helping them expand their repertoire.

Attracting younger music listeners to the courses I teach requires choosing a class time that is least likely to conflict with a prospective participant’s work schedule or—in the case of students—class schedule. For the courses I teach, I have generally settled on Saturdays from 1:00 – 2:30 p.m.

Trying to reach the people in the Tucson metro area that would most benefit from my music courses has proved exceedingly difficult. So far, almost all of my students have comes from a Meetup group I started (also in 2023) and the Tucson Masterworks Chorale, where I am a member of the tenor section. Ideally, I would like to reach Classical 90.5 listeners (AZPM) and those that attend Tucson Symphony Orchestra concerts, but neither AZPM nor TSO offer public service announcements for non-profit community music events, and the cost of advertising with them is prohibitively expensive for an individual of modest means. I charge $20 per person for each music course I teach, and that covers my cost of renting the venue and little more. I want my courses to be affordable to all. Yes, it is a labor of love, but how to reach those that would most benefit from what I am doing?

I spend about half a year preparing each course that I teach, working on it each and every day (except when I am out of town which happens much less frequently than I would like). Given the enormous amount of time I invest in preparing each course, it would be a shame if I never had the opportunity to further refine and teach these courses again. At the time of this writing, I am currently teaching a course on Gustav Holst with twelve participants, and I have four other courses ready to be taught again at any time: Johannes Brahms, Sergei Prokofiev, Antonín Dvořák, and Dmitri Shostakovich. Here’s a link for an up-to-date list of past, present, and future courses that I will be teaching:

Music for Listeners – Tucson

I am sure there must be others in the Tucson metro area who would like to teach for an organization that offers evening and weekend classes and thus is inclusive of both non-retired as well as retired folks. Right now, this is one of many unmet needs we have here in Southern Arizona.

UCAC4 379-071051: A Possible New Double Star Discovery

Shadow path of UCAC4 379-071051 during its occultation by asteroid 2392 Jonathan Murray on April 18, 2025 UT

On April 18, 2025 UT, I observed an occultation of the 11.9-magnitude star (mv) UCAC4 379-071051 in the constellation Libra by the 17.7-magnitude asteroid (mv , at the time of observation) 2392 Jonathan Murray.

As you can see in the light curve below, I observed a two-dip event. Since the magnitude drops are unequal, that rules out an asteroid satellite.

2392 Jonathan Murray apparently covered up the brighter component of a heretofore unknown double star (either binary or optical), followed by a brief interlude before the fainter component was covered up.

The magnitude drop when the fainter star was occulted was 0.44. When the brighter star was occulted, the magnitude drop only goes down as far as the limiting magnitude of my sky in the images, which was around 14th magnitude (Tucson is not as dark as it once was). Using the magnitude drop when the fainter component was being covered by the asteroid (the only reliable magnitude drop we have), and knowing the magnitudes of the two components must sum to 11.9 magnitude, we can calculate that the magnitude of the two components are:

Primary Component (1st star occulted): 12.34

Secondary Component (2nd star occulted): 13.09

Occultation analysis expert Dave Gault (Australia) used my light curve and knowledge of the asteroid’s size and motion (and all the other factors that need to be considered) to provide the following preliminary double star solutions (there was not enough information for a single solution):

Double Star Solution #1
Separation = 36.9 mas
Position Angle = 103.6°

Double Star Solution #2
Separation = 37.0 mas
Position Angle = 113.8°

These two solutions are quite close to one another. Averaging the two separations, we get 36.95 milliarcseconds. Gaia DR3 indicates that the parallax of this star is 1.323 milliarcseconds. That’s a distance of almost 756 parsecs or 2,500 light years. At that distance, these two stars have an apparent separation (in the plane of the sky, so a minimum) of 28 AU, or a little less than the distance between the Sun and Neptune in our own solar system. This is not unreasonable for a true binary star system, but, of course, the fainter star could be many light years further away than the brighter star (which is presumably the component Gaia measured in determining the parallax). In that case, this would just be a chance alignment of two stars at different distances but not physically associated with one another.

High-resolution spectroscopic observations of UCAC4 379-071051 over time could determine whether or not this is a true binary star system. Astrometric measurements over time with whatever supercedes Gaia (likely) or analysis of occultations of this star by other asteroids (unlikely) could also determine whether or not these stars are a true binary star system.

Confounding factors in the double star solutions include (1) We don’t know the exact size of asteroid 2392 Jonathan Murray (Neowise gives a diameter of 6.5 miles); (2) We don’t yet know the shape or orientation (at event time) of this asteroid (my occultation observation was the first time this asteroid has been observed to occult a star); (3) We don’t know the orientation of my single observation chord (what part of the asteroid crossed the two stars).

As you can see, there’s a lot to consider in trying to interpret this atypical (though not all that unusual) “double dip” occultation event. Of course, the very first thing we did was to rule out any terrestrial cause of the second smaller dip (clouds, for example), and we had to also rule out any equipment anomalies that could have caused the second smaller dip (CCD anomalies, for example). After convincing ourselves that this was a real event, we proceeded with the analysis. A big thank you to Dave Gault and Dave Herald in Australia for their work and expertise in analyzing this data!

American Democracy in Crisis: Solutions

American democracy is certainly beginning to show its age and we could learn a thing or two from some of the newer democracies elsewhere in the world that have made improvements.

Here, I would like to offer what I believe are the two most important changes we can make to governance in the United States that will make government work better for all citizens and that will help reduce the polarization that is currently paralyzing our country.

#1 Publicly Financed Political Campaigns

Each accepted candidate for an elected political office should receive a designated amount of taxpayer-funded money for their campaign and not be allowed to accept donations from individuals, corporations, lobbyists, special interest groups, or any other entity. Key aspects of these publicly financed political campaigns would be

  • At each level of government (local, county, state, national) each candidate would need to receive an agreed-upon minimum number of nomination petition signatures in order to qualify for a run.
  • The amount of money each candidate receives depends on the office and the level of government, with national candidates receiving the most financial support.
  • There will be agreed-upon rules on how this money can be used and transparency into how it is used.
  • All candidates for a given political office receive the same amount of money to fund their campaigns.
  • Though each candidate is barred from accepting donations from other sources, they are free to take part in as many interviews and debates sponsored by other organizations as they wish.

#2 Ranked Choice Voting

Ranked Choice Voting (also known as instant runoff) allows each voter to vote for more than one candidate by selecting their first choice, second choice, and so on, if they wish. Ranked Choice Voting should be allowed at all levels of government (local, county, state, and national).

Here’s a simple example of how one method of ranked choice voting works.

Let’s say you have three candidates running for a particular political office: Candidate A, Candidate B, and Candidate C.

There are nine different ways a voter could vote in this election:

A only
B only
C only

First choice: A; Second choice: B
First choice: A; Second choice: C
First choice: B; Second choice: C
First choice: C; Second choice: B
First choice: C; Second choice: A
First choice: B; Second choice: A

Now, let’s say we have 8,764 voters who voted as follows:

A only: 182
B only: 361
C only: 880

A, then B: 718
A, then C: 1,366
B, then C: 1,336
C, then B: 1,815
C, then A: 489
B, then A: 1,617

Tallying up everyone’s first choice gives us:

Candidate A: 182 + 718 + 1,366 = 2,266 votes
Candidate B: 361 + 1,336 + 1,617 = 3,314 votes
Candidate C: 880 + 1,815 + 489 = 3,184 votes

We see that Candidate A received the fewest votes, so they are removed from further consideration. We now look at the second choice (if any) of all those who voted for Candidate A as their first choice, in addition to those who voted for Candidates B & C as their first choice.

Candidate B: 361 + 718 + 1,336 + 1,617 = 4,032 votes
Candidate C: 880 + 1,366 + 1,815 + 489 = 4,550 votes

You’ll notice the 4,032 + 4,550 = 8,582 votes, which is 182 less than the total number of voters (8,764). That’s because 182 voters voted only for Candidate A, and since they didn’t specify a second choice, when Candidate A was removed their contribution to the election is over at this point.

You’ll also notice that Candidate C wins the election with the majority of the votes (4,550 vs. 4,032).

Generalizing, if there are n candidates running then the number of ranked choices available is n-1. For example, for four candidates, there would be two rounds of elimination instead of only one as shown in the three-candidate example above.

Two candidates qualifying
Each voter chooses one and only one candidate

Three candidates qualifying
Each voter can choose a first choice and second choice candidate

Four candidates qualifying
Each voter can choose a first choice, second choice, and third choice candidate

And so on…

Ranked choice voting would encourage more than two viable political parties (and that would be a good thing, seeing as our current two-party system maximizes polarization), plus voters could vote for any candidate they truly support without fear of the spoiler effect, since they can specify a second choice should their first-choice candidate be eliminated because they received fewer votes than the other candidates.

It is unlikely that initiatives to adopt publicly financed political campaigns and ranked choice voting will come from either the Republican or Democratic parties (or their corporate and billionaire donors and lobbyists!) so it is up to us, the rank-and-file voters, to force these issues at a grassroots level. I would be interested in hearing from readers who have ideas on how best to accomplish this.

Nearest Exoplanets

There are 33 confirmed exoplanets within 15 light years of our solar system, with more certainly on the way as a number of unconfirmed exoplanets are under ongoing investigation.

Here’s a table of all known planets within 15 light years of the Sun, including the eight planets of our own solar system for comparison.

Click the link below for a more convenient view of the entire table in a separate tab.

Click to access Nearest-Exoplanets-Confirmed-Planets.pdf

Planet mass and radius are given in terms of Earth’s mass and radius. The reason the radius of all the exoplanets listed here is “unknown” is because all of these planets have been detected using the radial velocity and/or astrometric method. Only the transit method provides a reliable way to measure an exoplanet’s size, but the nearest stars that host transiting exoplanets are 21.3 ly and 22.4 ly distant (HD 219134 and LTT 1445, respectively). Our limit here is 15 ly.

A side note about transiting exoplanets. In order for us to see an exoplanet transiting its host star, the exoplanet’s orbital plane has to be fortuitously aligned quite close to our line of sight. Since even these nearest stars are very far away in comparison to the size of our solar system, we are stuck with the line of sight we have. What percentage of all exoplanets out there might we detect using the transit method? That depends, of course, on the orientation of the exoplanet’s orbital plane but also the size of the star (and the planet if it is large) and the distance of the exoplanet from that star. Roughly, only about 1 in 200 exoplanets or about 0.5% can be detected using the transit method.

Luminosity is the host star’s luminosity in terms of our Sun’s luminosity. Bolometric luminosity is used where available; otherwise, optical luminosity is used.

The average distance of the planet from the star is calculated from the semi-major axis and the orbital eccentricity. We then calculate the incident stellar flux using the average distance of the planet from the star and the luminosity of the star, normalized to what the Earth receives (0.9997 and not 1.oooo because the Earth, on average, is more than 1 AU from the Sun). The relevant equation is:

\frac{\textrm{L}}{\bar{\textrm{d}}^{2}}\cdot\phi_{\oplus }

where L is the luminosity of the star in terms of the Sun’s luminosity
   and d-bar is the average distance of the planet from the star in AU
   and Φ⊕ is the incident stellar flux at Earth’s average distance from the Sun
             in proportional units of solar luminosities per AU2

This calculation, of course, makes no assumptions about the albedo of the planet nor whatever atmosphere the planet may or may not have. It is simply a calculation of stellar radiation per unit area received at the planet’s distance from the star.

Here’s an example from the table. Mercury, on average, receives 6.4 times as much energy per unit area as does the Earth, whereas Neptune receives only 0.0011 as much as the Earth.

Some Key Takeaways

  • The most luminous star that is known to host exoplanets within 15 light years of our solar system, Epsilon Eridani, is only 32% as bright as the Sun.
  • Eight of these exoplanets receive an amount of energy from their star that is comparable to what the Earth receives from the Sun: Gliese 1061 d (0.56), Proxima Centauri b (0.66), Gliese 687 b (0.78), Luyten’s Star b (1.05), Teegarden’s Star b (1.07), Wolf 1061 c (1.37), Gliese 1061 c (1.40), and Ross 128 b (1.42).
  • The most massive of these exoplanets is Epsilon Eridani b, weighing in at 311 earth-masses, comparable to Jupiter in our own solar system (318).

I’d like to conclude by noting that I will do my best to keep this table up-to-date, but if you see something that needs changing before I do, by all means post a comment here and I will make the correction or addition.