The Electromagnetic Spectrum

What do light, radio waves, and x-rays have in common? Everything! They are all electromagnetic radiation which differ only in their frequency, wavelength, and energy. All electromagnetic radiation travels at the speed of light, which in a vacuum is 186,282 miles per second or almost 671 million mph.

There are no distinct boundaries between different regions of the electromagnetic spectrum. The spectrum can, however, be conveniently divided into the following seven general categories (in order of decreasing energy and increasing wavelength): gamma rays, x-rays, ultraviolet, visible, infrared, microwave, and radio.

Depending on how it is observed, all electromagnetic radiation has a dual nature, capable of behaving either as a wave or as a particle. We call these particles photons. The highest energy photons are gamma ray photons, and the lowest energy photons are radio wave photons.

The highest-energy, shortest-wavelength electromagnetic radiation (gamma rays and x-rays) usually behaves like a particle rather than a wave in experiments, whereas the lowest-energy, longest-wavelength electromagnetic radiation (radio waves) usually behaves like a wave in experiments.

Is there a limit to how far the electromagnetic spectrum extends? On the high energy end, we think so. On the low energy end, not really. Let’s explore both extremes.

Gamma rays are produced by the most energetic processes in the universe. The highest energy gamma rays yet detected are 2.5 PeV (2.5 peta-electronvolts or 2.5 × 1015 eV). The theoretical limit to the energy of a gamma ray is the Planck energy, 12.2 ReV (12.2 ronna-electronvolts or 1.22 × 1028 eV). Any gamma ray having this much energy would have a wavelength of a Planck length (1.6 × 10-35 meter). At this wavelength, standard quantum physics breaks down and the gamma ray photon would concentrate so much energy into so small a space that it would likely collapse into a microscopic black hole, ending its existence as radiation.

There is another, much lower energy limitation, however. At gamma ray photon energies around 0.1 to 100 PeV (1014 – 1017 eV), the universe becomes almost completely opaque over large distances. A gamma-ray photon at this extreme energy will travel only a short distance before colliding with a photon from the pervasive cosmic microwave background. This collision converts the original photon into an ultra-relativistic electron-positron pair. As these new particles hurtle through space, they smash into additional background photons via inverse Compton scattering, boosting them into high-energy gamma rays. This triggers an energy-diluting electromagnetic cascade: photons create particle pairs, and particle pairs produce new photons. The chain reaction repeats until the individual photon energies drop below the threshold required for pair production. The end result: the original high-energy gamma ray photon never reaches your detector.

Now, let’s talk about the opposite end of the spectrum, the radio waves. What do we know about the least energetic of photons? To put things in perspective, you may be interested to know that national and international standards have been established for the orderly use of the radio spectrum down to a frequency of 3 kHz (3000 Hz), although the military is using 40 – 80 Hz radio waves for global submarine communications, and every electrical wire in your house is generating low levels of 60 Hz radio waves due to alternating current flipping back and forth 120 times each second.

Below 40 Hz exists a strange realm indeed. The Earth and its atmosphere act like a giant, natural radio transmitter. Lightning storms continuously bombard the upper atmosphere and trigger extremely low frequency radio waves (known as Schumann resonances) that ring around the globe at roughly 7.5 Hz.

To generate radio waves with even lower frequencies than 7.5 Hz, the scale of the “antenna” must grow to planetary proportions. In nature, this occurs when exceptionally energetic lightning events or the shockwaves from large meteors dump enormous energy into the atmosphere, creating radio waves with frequencies of 3 Hz or lower. The immense mechanical stress of shifting fault lines before an earthquake can turn miles of quartz-rich bedrock into a colossal subterranean transmitter, broadcasting seismic radio pulses down to a fraction of a hertz via the piezoelectric effect. Humans can replicate this feat artificially, but the physical constraints are staggering. For example, a 1 Hz wave has a wavelength of nearly 300,000 kilometers. Efficient transmission requires an antenna of comparable size.

There is no theoretical lower limit to a radio wave’s frequency. Any accelerating electrical charge can produce one, and if the system that produces it is large enough, natural processes can generate radio waves with frequencies as low as a nanohertz (a billionth of a Hz), or even lower, resulting in wavelengths measured in light-years.

We can only study these ultra low frequency radio waves which are of a cosmic origin from space because the Earth’s ionosphere reflects away everything below about 5 MHz. But we’ll have to travel far from the Sun if we wish to listen to cosmic radio frequencies below about 20 kHz because the solar wind acts as a reflective shield. Only by traveling beyond the heliopause and into interstellar space will we escape the Sun’s plasma shield, though the ambient interstellar medium itself will still block frequencies below 2 kHz. In order to listen to the cosmic din and chatter at sub-Hertzian frequencies, you’d have to find a completely empty intergalactic void entirely cleared of plasma.



Here are the wavelength ranges of our currently operating general purpose space telescopes (1 Å = 1 angstrom = 0.1 nm = 0.1 nanometer = 10-10 m).

Fermi Gamma-ray Space Telescope
0.000000041 → 1.55 Å

Chandra X-Ray Observatory
1.20 → 120 Å

Hubble Space Telescope                         Visible Spectrum
1150 → 17,000 Å                                           3800 → 7500 Å          (blue → red)

James Webb Space Telescope
6000 → 283000 Å

There are currently no active general purpose space telescopes operating in the 120 Å to 1150 Å range (between Chandra and Hubble). This is known as Extreme Ultraviolet (EUV), the transition zone between the ultraviolet and x-ray parts of the electromagnetic spectrum. However, space telescopes that observe the Sun do observe in the EUV region.

Because neutral hydrogen in the interstellar medium is highly efficient at absorbing EUV radiation, galactic and extragalactic objects are difficult or impossible to observe at these wavelengths, especially between 400 Å and 912 Å.

There are currently no general purpose space telescopes observing at wavelengths longer than 283000 Å (James Webb), in the far-infrared and radio part of the spectrum.

To detect far-infrared and submillimeter (shortest-wavelength radio) radiation requires a space telescope to be cooled to nearly absolute zero. This is challenging but not impossible.

The Earth’s atmosphere is adequately transparent to most radio waves, so observing this part of the electromagnetic spectrum from the Earth’s surface is easier and cheaper than building a radio space telescope. However, the far side of the Moon would be an even better location to observe almost the entire radio spectrum (except for the short-wavelength submillimeter radiation which requires extreme cooling as mentioned above), both because the Moon lacks an atmosphere but also because terrestrial radio interference would be completely blocked.

Inconvenient Truths

Our Current Human Population is Unsustainable

All attempts to address the effects of human-induced climate change, the loss of biodiversity, and environmental pollution will utterly fail without a substantial reduction in human population.

The only acceptable method to reduce human population will require a substantial number of people opting for one child or no children.

Those of us alive today are burning through the Earth’s natural resources and polluting the environment (our environment) with toxic substances at a rate that is unsustainable for another one or two generations let alone a hundred. This aspect of overpopulation doesn’t get enough attention, and is exactly why our current population is an existential threat that must be addressed immediately and decisively by all nations of the Earth.

We Have Too Many Pets

The number of dogs and cats and other pets worldwide is exacerbating the effects of human overpopulation significantly.

The Second Amendment to the U.S. Constitution Needs to be Repealed and Replaced

The Second Amendment to the U.S. Constitution was enacted in 1791. Much has changed since then! As written, the amendment is too general and does not take into account current realities of gun ownership and use.

The current interpretation of the Second Amendment is a moral and humanistic abomination.

Michael Moore has proposed a 28th amendment to the U.S. Constitution which should seriously be considered, at least as a starting point.

We Need Binding International Laws

Globally, we must work toward establishing a global “super-government” that enacts and enforces binding international laws that are in the best interest of all the world’s peoples. Individual nations will have to give up some sovereignty in order to effectively address global threats such as nuclear weapons, warfare, human rights violations, pandemics, climate change, pollution, environmental degradation, loss of biodiversity, cybercriminality, and, yes, the proliferation of Earth-orbiting satellites. Whether the United Nations can be strengthened to serve in this role or a new organization created will need to be explored.

There is No Evidence for the Existence of God

Why does the world have thousands of religions? Why do bad things happen to good people and good things happen to bad people? The most sensible explanation is that religion is entirely a human creation based on basic human wants and needs and that there are no supernatural forces actively present in our daily lives.

The greatest of all mysteries is why does our universe exist and how did it come into being? Religion tries to answer these questions, of course, but I think it more likely that our intellect (as amazing as it is) is incapable of fully comprehending these questions let alone the answers. We have only our empirical knowledge of our world (and the universe) and our moral pragmatism (humanism) to guide us.

There is No Evidence for the Existence of an Afterlife

Regarding immortality, since we have no consciousness of anything before we were born, why should we expect that we would have any consciousness of anything after we die? To me, that is the most tragic fact of human existence. Within a few minutes (or hours, if extraordinary measures are taken) after death occurs, all of our knowledge and experience—our memories—everything that makes us who we are—is irretrievably lost. All that remains of us are the artifacts we have left behind (writing, music, art, etc.) and the memories of those who are still living who knew us. After all the people who knew us personally have died, then all that remains of our existence are artifacts. And, sooner or later, all of those will be gone, too. This truly emphasizes the importance of this life, of this world, of this time. How we live our lives and treat others today, tomorrow, and the next day are of paramount importance. It is all we have, or will ever have.

Not believing in God and not believing in an afterlife is incredibly liberating, and allows us to see our world and our lives through less varnished eyes.

Classical Music Timeline: 1760s

This is one of a series of postings of important classical music dates, from the 17th century to the present. Included are the date and location of the birth and death of composers, and the premiere date and location of the first public performance of works. When the premiere date and location is unknown, the date or year of completion of the work is given. Though reasonably comprehensive, this is a subjective list, so the choice of composers and works is mine. If you find any errors, or if you can offer a premiere date and location for a work where only the completion date or year is listed, please post a comment here.

1761
Joseph Haydn (1732-1809) completed Symphony No. 6 in D major, Hob. I:6 “Le matin”

1762
Antonio Sarrier (1725-1762) died in Spain (specific location, unknown)

1764
Joseph Haydn (1732-1809) completed Symphony No. 22 in E-flat Major, Hob. I:22 “The Philosopher”

After October 25 – Wolfgang Amadeus Mozart (1756-1791) wrote Violin Sonata No. 6 in G major, K. 11 (while in London, England)

1765
February 21 – Symphony No. 1 in E♭ major, K. 16 by Wolfgang Amadeus Mozart (1756-1791) was first performed in London, England

1766
January 22 – Symphony No. 5 in B♭ major, K. 22 by Wolfgang Amadeus Mozart (1756-1791) was first performed in The Hague, the Netherlands

March 11 – Gallimathias musicum, K. 32 by Wolfgang Amadeus Mozart (1756-1791) was first performed in The Hague, the Netherlands

1767
December 30 – Symphony No. 6 in F major, K. 43 by Wolfgang Amadeus Mozart (1756-1791) was first performed in Brno, Czech Republic

1768
Wolfgang Amadeus Mozart (1756-1791) completed the one-act singspiel, the comic opera Bastien and Bastienne, K. 50

1769
August 8 – Cassation in B♭ major, K. 99 by Wolfgang Amadeus Mozart (1756-1791) was first performed in Salzburg, Austria

←Before 1760

1770s→

More Perfect Than Earth

Did you know that both Venus and Neptune have orbits around the Sun that are more circular than the orbit of the Earth? In fact, Venus has the most circular orbit of all the major planets in the solar system. Here are the current orbital eccentricities of these three planets.

Venus0.007
Neptune0.010
Earth0.017

Perhaps surprisingly, there are currently 1,959 minor planets with orbits more circular than that of Venus. There may be more, but I’ve excluded any minor planets where the 1σ uncertainty in eccentricity is greater than the eccentricity itself. Large uncertainties happen because some minor planets do not yet have well-determined orbits.

To ensure that my restriction of σe < e wouldn’t be too severe, I confirmed that minor planet 232812 has the lowest known orbital eccentricity. The 11 minor planets that nominally have a lower eccentricity are all unnumbered, which means their orbits are not well determined and should thus be excluded.

The most circular orbit of all minor planets with a well-determined orbit is 232812 (2004 RG298). It has not yet received a name. It is a main-belt asteroid and has an amazingly circular eccentricity (e) of 0.0000152412. It orbits at a distance of 2.37 AU from the Sun once every 3.65 years. Its orbit is inclined 2.4° to the ecliptic. Its physical size is unknown

Among the named minor planets, the one with the most circular orbit is 12083 Darone. It is also a main-belt asteroid and has an eccentricity of 0.00177265. It orbits at a distance of 2.13 AU from the Sun once every 3.11 years. Its orbit is inclined 2.6° to the ecliptic. 12083 Darone has a diameter between 3.5 and 3.8 km. The lucky person to have this asteroid named after them is Gregory Darone, who mentored a finalist in the 2019 Regeneron Science Talent Search, a science competition for high school seniors. He teaches chemistry at the Charter School of Wilmington, Wilmington, Delaware.

The two largest trans-Neptunian objects are Pluto and Eris—both with high orbital eccentricities—and among the major planets, Mercury has the highest orbital eccentricity. Here are their current values.

Eris0.438
Pluto0.245
Mercury0.206

Eris has the highest orbital eccentricity of these three objects by far. Eris orbits between 38.2 and 97.7 AU from the Sun. Its current distance is 95.5 AU and it is very gradually getting closer to the Sun. At times during their respective orbits, Eris can be closer to the Sun than Pluto. Eris orbits the Sun once every 559.9 years at an orbital inclination of 43.9° with respect to the ecliptic.

Pluto orbits between 29.6 and 48.7 AU from the Sun. Its current distance is 35.6 AU and it is gradually getting further from the Sun. During the years 1979 to 1999, Pluto was closer to the Sun that Neptune, and this will next happen again from 2223 to 2243 (approximately). Pluto orbits the Sun once every 244.7 years at an orbital inclination of 17.0° with respect to the ecliptic.

Mercury orbits between 0.31 and 0.47 AU from the Sun. Mercury orbits the Sun once every 88 days at an orbital inclination of 7.0° with respect to the ecliptic.

All three of these objects are smaller than Jupiter’s moon Ganymede!

Incidentally, there is no known minor planet that orbits completely inside the orbit of Mercury, but (as of this writing) 523 asteroids and 1,608 comets have come closer to the Sun than Mercury ever does. Sometimes a comet comes so close to the Sun that it disintegrates completely. Actual collisions with the Sun do occur.

Getting back to our original topic of nearly-circular orbits, the Earth’s orbital eccentricity has ranged from as circular as 0.000055 to as elliptical as 0.0679 due to gravitational perturbations caused by all the other objects in our solar system. This variation in orbital eccentricity is one of the Milankovitch cycles. Currently, the Earth’s orbital eccentricity is becoming more circular.

The orbits of all objects in our solar system change with time (albeit usually gradually and by a gentle amount). Over millions or billions of years, the gravitational attraction from stars passing close to the solar system can nudge orbits, too. Our solar system is a much more dynamic place than anyone imagined a century ago. Barring the extremely unlikely event of a star (lots of advance warning) or a rogue black hole (much less advance warning) entering our solar system, the Earth’s orbital eccentricity should remain stable for a very long time to come.

Fred Gwynne

I watch very little television—almost entirely documentaries and news—but I must admit that every once in a while I like to dip into happier times through my living-room Atavachron to watch episodes from two 1960s television series1 starring the much-beloved 6 ft. 5 in. actor Fred Gwynne (1926-1993). The first is Car 54, Where Are You? (1961-1963), and the second is The Munsters (1964-1966). I am old enough to remember watching The Munsters during prime time when it originally aired, but I am too young to remember Car 54, Where Are You?, which I only recently discovered. I must admit I’m a fan of this talented actor.

Here are my favorite episodes from Car 54, Where Are You?:

Car 54, Where Are You?

Season 1, Episode 5: I Won’t Go
[This is the first time Fred Gwynne and Al Lewis (1923-2006) appear together on screen, beginning a tremendous partnership between these two great actors in both comedy series.]

Season 1, Episode 6: Muldoon’s Star

Season 1, Episode 11: Catch Me on the Paar Show

Season 1, Episode 14: Get Well, Officer Schnauser

Season 1, Episode 15: Christmas at the 53rd

Season 1, Episode 18: Toody & Muldoon Crack Down

Season 1 , Episode 20: How High Is Up?

Season 1, Episode 21: Toody and the Art World

Season 1, Episode 24: Today I Am a Man

Season 1, Episode 26: The Beast Who Walked the Bronx

Season 2, Episode 9: Toody Undercover

Season 2, Episode 10: I Hate Captain Block

Season 2, Episode 13: 142 Tickets on the Aisle

Season 2, Episode 20: Here We Go Again

Season 2, Episode 22: The Biggest Day of the Year

Season 2, Episode 23: Here Comes Charlie

Season 2, Episode 24: See You at the Bar Mitzvah


And, here are my favorite episodes from The Munsters:

The Munsters

Season 1, Episode 3: A Walk on the Mild Side

Season 1, Episode 7: Tin Can Man

Season 1, Episode 33: Lily Munster—Girl Model

Season 1, Episode 35: Herman’s Happy Valley

Season 2, Episode 17: Just Another Pretty Face

Season 2, Episode 24: The Musician

Fred Gwynne 1984 . Credit: Ralph Dominguez/MediaPunch

  1. While we are on the topic of great television series from the 1960s, please see my lists of favorite episodes from the greatest of them all: The Twilight Zone (1959-1964) and Star Trek (1966-1969):
    The Twilight Zone
    Star Trek ↩︎

Interstellar Visitors

As of this writing, three objects have been discovered that have passed through our solar system coming from interstellar space.

1I/’Oumuamua
Discovery Date: 2017-10-19
Perihelion Date: 2017-09-09 (40 days after perihelion)
Perihelion Distance: 0.26 AU
Incoming and Outgoing Speed: 26.4 km/s
Dimensions: approximately 115 m × 111 m × 19 m, or 230 m × 35m × 35m
Object Type: asteroid?

2I/Borisov
Discovery Date: 2019-08-29
Perihelion Date: 2019-12-08 (101 days before perihelion)
Perihelion Distance: 2.01 AU
Incoming and Outgoing Speed: 32.3 km/s
Diameter: 400 m – 1000 m
Object Type: comet

3I/Atlas
Discovery Date: 2025-07-01
Perihelion Date: 2025-10-29 (120 days before perihelion)
Perihelion Distance: 1.36 AU
Incoming and Outgoing Speed: 58.0 km/s
Diameter: 320 m – 5,600 m (most likely 520 m – 748 m)
Object Type: comet

Here are charts showing the direction from which each object entered our solar system, and the direction towards which each object is leaving our solar system.

1I/’Oumuamua came in from the direction of the constellation Lyra
1I/’Oumuamua is exiting in a direction inside the Square of Pegasus
2I/Borisov came in from the direction of the constellation Cassiopeia
2I/Borisov is exiting in the direction of the southern constellation Telescopium
3I/Atlas came in from the direction of the constellation Sagittarius
3I/Atlas is exiting in the direction of the constellation Gemini

1I/’Oumuamua
Incoming Right Ascension (2000): 18h 37m 53.88s
Incoming Declination (2000): +33° 51′ 34.7″
Outgoing Right Ascension (2000): 23h 51m 27.99s
Outgoing Declination (2000): +24° 42′ 33.0″
Angular Separation (Incoming→Outgoing): 67.4°
Deflection Angle: 180° – 67.4° = 112.6°

2I/Borisov
Incoming Right Ascension (2000): 2h 11m 37.54s
Incoming Declination (2000): +59° 27′ 26.6″
Outgoing Right Ascension (2000): 18h 21m 24.19s
Outgoing Declination (2000): -52° 00′ 21.9″
Angular Separation (Incoming→Outgoing): 145.4°
Deflection Angle: 180° – 145.4° = 34.6°

3I/Atlas
Incoming Right Ascension (2000): 19h 40m 04.79s
Incoming Declination (2000): -19° 04′ 21.7″
Outgoing Right Ascension (2000): 6h 20m 55.99s
Outgoing Declination (2000): +19° 48′ 15.6″
Angular Separation (Incoming→Outgoing): 161.3°
Deflection Angle: 180° – 161.3° = 18.7°

It is perhaps not surprising that 1I/’Oumuamua had the greatest deflection angle of the three interstellar objects. It came quite close to the Sun (0.26 AU, well inside the orbit of Mercury) and had the lowest incoming speed (26.4 km/s).

3I/Atlas, on the other hand, had the greatest incoming speed by far (58.0 km/s), so it was deflected by only 18.7° from a straight-line trajectory (angular separation 180° and deflection angle 0°).

International Characters on Your Keyboard

Here is how you can easily generate some common international characters on your computer keyboard.

CharacterMacintoshWindowsComments
á ÁOption-e a (or A)Control-‘ a (or A)Acute accent
à ÀOption-` a (or A)Control-` a (or A)Grave accent
ä ÄOption-u a (or A)Control-Shift-: a (or A)Umlaut
å ÅOption a (or A)Control-Shift-@ a (or A)Ring
â ÂOption-i a (or A)Control-Shift-^ a (or A)Circumflex
ã ÃOption-n a (or A)Control-Shift-~ a (or A)Tilde (Virgulilla)
æOption ‘Control-Shift-& aLigature (ae)
ÆOption-Shift ‘Control-Shift-& ALigature (AE)
çOption cControl-, c (or C)Cedilla
é ÉOption-e e (or E)Control-‘ e (or E)Acute accent
è ÈOption-` e (or E)Control-` e (or E)Grave accent
ë ËOption-u e (or E)Control-Shift-: e (or E)Umlaut
ê ÊOption-i e (or E)Control-Shift-^ e (or E)Circumflex
í ÍOption-e i (or I)Control-‘ i (or I)Acute accent
ì ÌOption-` i (or I)Control-` i (or I)Grave accent
ï ÏOption-u i (or I)Control-Shift-: i (or I)Umlaut
î ÎOption-i i (or I)Control-Shift-^ i (or I)Circumflex
ñ ÑOption-n n (or N)Control-Shift-~ n (or N)Tilde (Virgulilla)
ó ÓOption-e o (or O)Control-‘ o (or O)Acute accent
ò ÒOption-` o (or O)Control-` o (or O)Grave accent
ö ÖOption-u o (or O)Control-Shift-: o (or O)Umlaut
ø ØOption o (or O)Control-/ o (or O)O-Stroke
õ ÕOption-n o (or O)Control-Shift-~ o (or O)Tilde (Virgulilla)
ô ÔOption-i o (or O)Control-Shift-^ o (or O)Circumflex
œ ŒOption qControl-Shift-& oLigature (oe)
ŒOption-Shift QControl-Shift-& OLigature (OE)
ú ÚOption-e u (or U)Control-‘ u (or U)Acute accent
ù ÙOption-` u (or U)Control-` u (or U)Grave accent
ü ÜOption-u u (or U)Control-Shift-: u (or U)Umlaut
û ÛOption-i u (or U)Control-Shift-^ u (or U)Circumflex
ÿ ŸOption-u y (or Y)Control-Shift-: y (or Y)Umlaut

And, here are some common symbols you can generate on your keyboard.

CharacterMacintoshWindows*Comments
≈Option xAlt-247Approximately
•Option 8Alt-0149Bullet
°Option-Shift 8Alt-0176Degree
∆Option jAlt-916Delta
…Option ;Control-Alt-.Ellipsis
≥Option .Alt-242Greater Than or Equals To
∞Option 5Alt-236Infinity
≤Option ,Alt-243Less Than or Equals To
≠Option =Alt-8800Not Equals
πOption pAlt-227Pi
  • For Alt symbols in Windows, hold down the Alt key while typing the digits on the numeric keypad

Gravitational Lenses and Caustics

Credit:ESA/ESO/M. Kornmesser

A massive foreground object such as a galaxy or a galaxy cluster (including, of course, dark matter) can brighten and magnify a distant object. This is called gravitational lensing. Light from the distant object radiates out in all directions, but the massive foreground object bends some of these light rays towards the observer that normally would have continued on in a different direction, as shown in the illustration above.

The image we see is brighter because more light rays are directed our way. The image we see is also magnified because the gravitational lens gives the distant object a larger angular size, making it appear to be much closer to us. Again, the illustration above will help you understand why these effects occur.

Of course, unless the foreground object is a star or black hole or some other small spherical object with a reasonably uniform mass distribution, the gravitational lens effect will be complex and distorted, as illustrated below.

Gravitational lenses produce different shaped images depending on the shape of the lensing body. If the lens is spherical then the image appears as an Einstein ring (in other words as a ring of light) (top); if the lens is elongated then the image is an Einstein cross (it appears split into four distinct images) (middle), and if the lens is a galaxy cluster, then arcs and arclets (banana-shaped images) of light are formed (bottom). Credit: European Space Agency

There can be certain locations in a gravitational lens where light from a small region in the background becomes enormously magnified by a factor of up to 10,000 times. These regions are called caustics. Though the concept of a caustic is a bit difficult to describe or illustrate, here is a video of optical caustics caused by a laser pointer shining through a plastic disc with a lumpy surface.

References
How gravitational lensing acts as a magnifying glass — diagram

Different types of gravitational lenses

Caustic Projection Optical Element

Rodríguez, J. M. D. (2026). The First Stars. Scientific American, 334(2), 38. https://doi.org/10.1038/scientificamerican022026-2z1ygyIpj7gCMVn01NrfpU

Terrible Drivers, No Enforcement

Since moving to Tucson almost four years ago, my biggest complaint has to do with the terrible drivers and lack of enforcement of traffic laws. Here’s what I’ve noticed.

Speeding

  • Many drivers exceed the posted speed limit by +10 or +15 mph whenever they are not stuck in traffic; exceeding the speed limit by +20 mph is not uncommon.
  • Many of the drivers who exceed the speed limit constantly change lanes to get ahead; I often catch up to them at the next red light and even if not, how much time are they really saving while putting themselves and everyone around them in greater danger?
  • I have never seen one of these speeders and lane weavers pulled over by law enforcement.

Other Forms of Aggressive Driving

I’ve frequently experienced

  • A driver following too close behind a vehicle that is going the speed limit or slightly over, apparently in an effort to bully the law-abiding driver into either going faster or moving over to another lane (if that is possible) to let them through
  • A driver passing you in a no-passing zone
  • A driver cutting in front of you too soon after passing so that you have to brake to maintain a safe following distance
  • At night, lifted trucks and other large personal vehicles with blinding headlights; sometimes their “fog lights” are even brighter than their headlights.
  • Being honked at for not turning right on red soon enough to suit the driver behind you; sometimes this even occurs with left turns
  • Again, no enforcement.

Other Unsafe Driving Behaviors

  • Vehicles accelerating through an intersection while the traffic light is turning red; sometimes they do this after the light has turned red
  • Drivers running stop signs or only slowing down a little and not stopping before entering the intersection
  • Drivers not using their turn signals when switching lanes or making a right or left turn
  • Drivers driving without headlights during twilight and after dark
  • Drivers driving vehicles with a burned-out headlight; misaligned headlights are common, too
  • Again, no enforcement

City Life Makes People Crazy?

As a person who has lived most of my life in much smaller towns, I’ve noticed the following here:

  • A lack of driver courtesy; apparently city life brings out the worst in people when they get behind the wheel
  • For me, city life has taken all of the enjoyment out of driving.
  • The more dangerous the traffic conditions (due to traffic volume and/or a complex decision-making environment), the more aggressive drivers often become. Due to the elevated risk of a collision, drivers need to be more cautious in these situations—and many are—but there is often someone (usually a younger male) whose aggressive driving behavior puts themselves and everyone else in danger, including pedestrians and bicyclists (we have a very high pedestrian and bicyclist fatality rate here).
  • Posted speed limits are about +5 mph too high on many busy arterials with low access control. Most often, the posted speed limit is 40 or 45 mph when it should be 35 mph.

Safety Improvements

I’d like to see the following safety improvements.

  • At all signalized intersections with dedicated left turn lanes, only allow a left turn on green arrow (these are called protected left-turn lanes). I hate the flashing yellow arrow (turn left with caution) which may or may not be followed by a solid green arrow.
  • Prohibit right-turn-on-red
  • Prohibit U-turns at intersections; these are especially dangerous when combined with right-turn-on-red
Left-turn-on-green-arrow-only should be implemented at all signalized intersections with dedicated left turn lanes
U-turns should not be allowed at intersections where right-turn-on-red is allowed

Enforcement Improvements

I’d like to see the following enforcement improvements:

  • Hire more traffic law enforcement officers
  • Install red light cameras at signalized intersections
  • Use AI and other modern technologies to automatically detect traffic law violations and issue citations

I’ll conclude by stating that traffic law enforcement in Tucson, Arizona and the surrounding metro area is so lax that violators know they won’t get caught and that only encourages them to violate traffic laws even more. No wonder our auto insurance rates are so high here!

Oxygen Speaks with an Accent

There are three stable (non-radioactive) isotopes of the element oxygen:

  • 16O has 8 protons and 8 neutrons
  • 17O has 8 protons and 9 neutrons
  • 18O has 8 protons and 10 neutrons

All the oxygen in our solar system was forged in stars that existed before the birth of our Sun. The fusion processes that create oxygen from lighter elements require both high temperature and pressure. These conditions exist deep within a star. Different isotopes are created. A nucleus of an atom containing 8 protons identifies it as an oxygen atom, but it is the number of neutrons in the nucleus that determines which isotope it is. Not all isotopes are created in equal abundance.

When the solar system was forming, the oxygen in the “solar nebula” no doubt originally came from various progenitors. A supernova here or there, a planetary nebula somewhere else, and so on. As the solar nebula collapsed to form the Sun and planets, the relative abundance of oxygen to the other elements may or may not have been different in different parts of the solar nebula. Similarly, the relative abundances of the three stable isotopes of oxygen may also have been different in different parts of the solar nebula.

When we measure the relative amounts of the three oxygen isotopes in a terrestrial rock, ocean water, moon rocks, or the solar wind, it may tell us where the oxygen in those materials came from. It may also tell us something about the “life experiences” of the oxygen since the solar system formed. For example, water molecules containing 16O are more likely to evaporate than those water molecules containing the heavier isotopes 17O or 18O. Thus, ground water in the middle of a continent has a higher abundance of 16O than does water in the ocean.

When we look at the solar system today, we find significant differences in the relative abundances of the oxygen isotopes depending on where the material came from. On Earth, 99.75% of the oxygen atoms are of the 16O variety, 0.04% are 17O, and 0.21% are 18O, on average. We see very similar oxygen abundance ratios in moon rocks, indicating perhaps a common origin, but the oxygen abundance ratios in meteorites and solar wind particles are significantly different from this. For example, if you plot the 17O/16O ratio vs. the 18O/16O ratio for a bunch of terrestrial rocks, you get pretty much a straight line. Moon rocks fall along the same line. The calcium-aluminum-rich inclusions (CAI) and iron-magnesium-silicon chondrules in meteorites also form a straight line on this plot, but it has a distinctly different slope.

The solar wind samples collected by the Genesis spacecraft yielded abundances that fall along the same line as the CAIs and chondrules. Mars rocks fall on a line that parallels the Earth-Moon line, but is shifted upwards, indicating that for a given abundance of 18O, the Mars rocks will have a relatively higher abundance of 17O.