Centauri Dreams

Imagining and Planning Interstellar Exploration

Clearing the Air

I’ve played around a bit with Bluesky in the past, but have now decided it’s time to make a move. Those of you who have been following the site on X will want to know about the change, as posted in my first new Bluesky ‘skeet’ in some time. The change in user experience is striking, a bit like walking in an alpine meadow after spending years in a subway car. Not that I have anything against subways…

Have decided to move to BlueSky for good, having left X for obvious reasons. Future posts from my Centauri Dreams site will be linked here. Current post considers Clément Vidal's striking concept for using millisecond pulsars to move entire stellar systems. www.centauri-dreams.org/2024/11/14/a…

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— Paul Gilster (@gilster.bsky.social) November 16, 2024 at 8:30 AM

Addendum: For those who have asked, this affects only those of you who are connected to me on X, which I no longer use. If you don’t use X, nothing has changed in how you see Centauri Dreams.

A Millisecond Pulsar Engine for Interstellar Travel

Suppose you want to migrate to another star, taking your entire civilization with you. Not an easy task given our technology today, but let’s remember that in the 13 billion year-plus history of the Milky Way, countless stars and their planets have emerged that are far older than our 4.6-billion year old Sun. If we imagine an intelligence that survives for a billion years or more, we can hardly put constraints on what it might accomplish. The idea of moving a star with its planetary system intact is out there on the edge of what science fiction can accomplish, if not yet science. There have even been SETI searches for such projects, though as with SETI at large, no hits.

Why would you want to move a star? Consider that if you are a long-lived species with a simple interest in exploring the universe, setting up a journey in which you can take your culture with you – all of it – could have serious appeal. For one thing, you are also taking your primary energy source with you, and can now settle into a traveler’s frame of mind, confident of reaching exotic destinations sooner or later. Slow boat to the heart of the Laniakea Supercluster, and imagine the sights to be had along the way.

Imagine a culture in which extraordinarily long lifetimes – perhaps ‘immortality’ for a machine civilization – is the norm. The accelerated expansion of the universe will continue rendering some destinations unreachable. Dan Hooper, in a paper called “Life Versus Dark Energy: How An Advanced Civilization Could Resist the Accelerating Expansion of the Universe,” considered this in 2018; we’ll be looking at his ideas in the near future. Perhaps migrating to a globular cluster or into the tightly packed center of a galaxy would suggest itself as a goal worth achieving. But let’s not dig too far into motivations. What could humans possibly understand about the motivations of a billion-year old culture? Let’s just look for observables. So how about this:

Image: This is Figure 3 from the paper by Clément Vidal we’ll be discussing today. Caption: The original black widow pulsar PSR J1959+2048. Left: the BW pulsar (in blue) is plotted in the RA-DEC plane, and its proper motion vector is displayed until it reaches a close encounter with a target star, in orange, whose Gaia DR3 ID is displayed (see Vidal et al. 2023 [60] for the method used to find close encounters). Middle: a Chandra X-ray view of the BW pulsar, displaying a comet-like tail; the candidate target star is also visible in the bottom right (visualization with ESASky). Right: The composite image on the right shows the X-ray tail (in red/white) and a bow shock visible in the optical (green). Credit: X-ray: NASA/CXC/ASTRON/B. Stappers et al. [38]; Optical: AAO/J.Bland-Hawthorn & H.Jones; scale: 1.2 arcmin on a side.

We’ll get to the terminology involved in that caption in a moment. For now, is this conceivably a stellar engine in motion toward a nearby star? Probably not, but I introduce this image because I suspect that SETI searches for stellar engines are not well known, although they have been performed and we’ll be looking at these soon. And it also introduces the possibilities of an entirely different kind of stellar engine.

It’s no surprise that it should emerge through the work of Clément Vidal, given the philosopher’s long-standing interest in deep time and societies that go back to the early eons of the universe. Vidal (Center Leo Apostel, Vrije Universiteit Brussel, Belgium) is the author of the essential The Beginning and the End (2014) which along with his papers explores the terrain of matter and energy as a means of increasing order, and the possibility of locating ancient civilizations by finding what appear to be natural objects conceivably being manipulated by engineering on scales that we can only imagine.

Vidal’s latest plunges into what he calls the ‘Spider Stellar Engine,’ a steerable design using binary star pairs as parts of a propulsive system that uses one star as payload and the other as fuel. If this reminds you of Olaf Stapledon, you’re right, as it was he who wrote about artificial stars created to support interstellar voyaging in the 1930s. But I’m glad to see Vidal also pointing to Fritz Zwicky, who has all too often been overlooked in the history of exotic concepts even though it turns out that on matters like dark matter, he was far ahead of the game. Here’s Zwicky on stellar engines:

“Considering the Sun itself, many changes are imaginable. Most fascinating is perhaps the possibility of accelerating it to higher speeds, for instance 1,000 km/s directed toward α-Centauri in whose neighborhood our descendants then might arrive a thousand years hence. All of these projects could be realized through the action of nuclear fusion jets, using the matter constituting the Sun and the planets as nuclear propellants.”

Various science fiction authors have explored the concept, and Stanley Schmidt even came up with an assist from aliens offering to boost the Earth to another stellar system to save it in Sins of the Fathers (1977). But the most technically judicious treatment of moving an entire system like this is probably the one depicted in Greg Benford and Larry Niven’s Bowl of Heaven series, which in turn draws on the thinking of the Russian engineer and scientist Leonid Shkadov (1927–2003). As with Dyson spheres, here we are in the domain of engineering at a colossal scale.

Image: A Shkadov thruster at work. Credit: Greg School.

Let’s give Shkadov his due before exploring Vidal’s new concept. A Shkadov thruster works through a balancing act. A semi-spherical mirror is positioned in such a way that the pressure of solar photons balances the gravitational force of the star on the mirror. Achieve this and the radiation hitting the mirror reflects back toward the star, producing an imbalance that creates thrust. Here’s a diagram from a paper by Duncan Forgan (University of Edinburgh) that is the best I can find to illustrate the concept:

This is Figure 1 from Duncan Forgan’s paper “On the Possibility of Detecting Class A Stellar Engines Using Exoplanet Transit Curves (citation below).” The treatment of Shkadov thrusters is useful, and I insert the diagram here because the Vidal paper only offers a short explanation of the original concept. Forgan’s caption: Diagram of a Class A Stellar Engine, or Shkadov thruster. The star is viewed from the pole – the thruster is a spherical arc mirror (solid line), spanning a sector of total angular extent 2ψ. This produces an imbalance in the radiation pressure force produced by the star, resulting in a net thrust in the direction of the arrow. Credit: Duncan Forgan.

Clément Vidal brings into the stellar engine mix the idea of using binary millisecond pulsars. You may recall Vidal’s stellivore concept, which we’ve discussed over the years in Centauri Dreams. Here’s how he describes it in the current paper:

…the stellivore hypothesis, that reinterprets some observed accreting binary stars as advanced civilizations feeding on stars… The scenario would be the following. For most of its time, a stellivore civilization would eat its home star via accretion. However, energy is never eternal, and instead of eating its star until the end and dying, a stellivore civilization would use its low-mass companion star as fuel not to be accreted, but to be evaporated, in order to create thrust and travel towards a nearby star. The fundamental accretion dynamics of close binaries would be reversed into an evaporation dynamics.

In the new paper, Vidal homes in on so-called spider pulsars, which are binary systems made up of one millisecond pulsar and a low-mass companion star. This in itself has always struck me as an extraordinary situation. We’re positing a massive star in a binary system that becomes a supernova and leaves behind a neutron star. In many cases, the binary system (i.e., the companion star) survives this event, allowing the neutron star thereafter to draw material out of it through accretion. It’s this transfer of mass that ‘spins’ up the neutron star – this is simple transfer of angular momentum – so that the neutron star can rotate at millisecond rates.

I haven’t seen any figures on what percentage of binary systems can survive a supernova event, but it’s telling that a high proportion of millisecond pulsars are indeed found in binary systems. Millisecond pulsars (MSPs) are detectable when the beam of electromagnetic radiation they emit sweeps past our observing apparatus.

Image: This diagram shows the steps astronomers say are needed to create a pulsar with a superfast spin. 1. A massive supergiant star and a “normal” Sun-like star orbit each other. 2. The massive star explodes, leaving a pulsar that eventually slows down, turns off, and becomes a cooling neutron star. 3. The Sun-like star eventually expands, spilling material on to the neutron star. This “accretion” speeds up the neutron star’s spin. 4. Accretion ends, the neutron star is “recycled” into a millisecond pulsar. But in a densely packed globular cluster (2b)… The lowest mass stars are ejected, the remaining normal stars evolve, and the “recycling” scenario (3-4) takes place, creating many millisecond pulsars. Credit: B. Saxton, NRAO/AUI/NSF.

A spider pulsar as described by Vidal is made up of a one millisecond pulsar and a relatively small companion. And here we get the unusual evaporation effect that the above quote references. Rather than accreting matter from the companion star, a spider pulsar system evaporates the companion star. Hence the ‘spider’ metaphor, referring to female spiders that eat their male companion after mating. Get the right configuration and you have what Vidal calls a spider stellar engine. How it can be used to accelerate, decelerate and steer over interstellar distances takes up much of the paper. More on that next time.

In this kind of engine, the payload is a neutron star of about 1.8 solar masses. The propellant is the low-mass companion star somewhere between 0.01 and 0.7 solar masses. And where are the passengers; i.e., the civilization that is transporting itself around the galaxy? We have a lot to discuss here, and I also want to dig into the Hooper paper referenced above as well as the subject of hypervelocity stars, which are possible instances of stellar engineering technosignatures. We continue next time, with an email exchange I’ve been having with Vidal and the fine-tuning of stellar engines.

Clément Vidal’s new paper is “The Spider Stellar Engine: a Fully Steerable Extraterrestrial Design?” Journal of the British Interplanetary Society Vol. 77 (2024), 156-166 (preprint). Leonid Shkadov’s original paper on the Shkadov thruster is “Possibility of controlling solar system motion in the galaxy,” 38th Congress of IAF,” October 10-17, 1987, Brighton, UK, paper IAA-87-613. The Forgan paper is “On the Possibility of Detecting Class A Stellar Engines Using Exoplanet Transit Curves,” accepted at the Journal of the British Interplanetary Society (preprint).

Habitability and a Variable Young Sun

Given our intense scrutiny of planets around other stars, I find it interesting how little we know even now about the history of our own Sun, and its varying effects on habitability. A chapter in an upcoming (wildly overpriced) Elsevier title called The Archean Earth is informative on the matter, especially insofar as it illuminates which issues most affect habitability and how the values for these vary over time. It’s also a fascinating look at changing conditions on Venus, Earth and Mars.

We know a great deal about the three worlds from our local and planetary explorations, but all too little when it comes to explaining the evolution of their atmospheres and interior structures. But it’s important to dig into all this because as Stephen Kane, director of The Planetary Research Laboratory at UC-Riverside and colleagues point out, we seem to be looking at the end state of habitability on both Mars and Venus, meaning that our explorations of these worlds should yield insights into managing our own future. Powerful lessons are likely to emerge, some obvious, some obscure.

The chapter title is “Our Solar System Neighborhood: Three Diverging Tales of Planetary Habitability and Windows to Earth’s Past and Future” (citation below), from which this:

Resolving the numerous remaining questions regarding the conditions and properties of our local inventory of rocky worlds is… critical for informing planetary models that show how surface conditions can reach equilibrium states that are either temperate and habitable, or hostile with thick and/or eroded atmospheres.

Given the challenges of working at the Venusian surface, Mars is particularly valuable as a case study, a world that has evolved through a period of habitability (is this true of Venus?) and undergone interior changes including cooling, not to mention loss of atmosphere. The more we learn about the evolution of rocky worlds, the more we will be able to apply these discoveries to planets around other stars. We’re in search of models, in other words, that show how planets can reach equilibrium as habitable or hostile.

The Archean eon (roughly 4 to 2.5 billion years in extent) takes us through the formation of landmasses, Earth’s early ‘reducing’ atmosphere (light on oxygen but rich in methane, ammonia, hydrogen carbon dioxide) and all the way to the emergence of life. So we have plenty to work with, but for today I want to focus on one aspect of habitability that we haven’t discussed all that often, the changes in the Sun since Earth’s formation. Our G-class star had to progress through a protostar stage lasting, perhaps, 100,000 years or more, then a T-tauri phase likely lasting 10 million years. There’s a lot going on here, including shedding angular momentum as the young Sun expels mass, slowing its rotation rate and producing a powerful solar wind.

The Sun’s arrival on the main sequence follows, and we’re immediately involved in a singularly vexing astronomical puzzle. The consensus seems to be that the early main sequence Sun was only about 70 percent as bright as the star we see today. That being the case, how do we account for the fact that water appears early in Earth’s history in liquid form on the surface? The expectation of a frozen world is a natural one, yet liquid water at the surface seems to have been available for some four billion years.

Image: The landscape during the early Archean could have looked like this: small continents on a planet mostly covered by oceans, illuminated by the much fainter young Sun, and with a Moon that appears larger in the sky because of its smaller distance to Earth. Credit: Potsdam Institute for Climate Impact Research.

Infant stars in the T-tauri phase are quite bright, getting their energy primarily from gravitational contraction. When they reach the main sequence and hydrostatic equilibrium sets in, they are considerably dimmer. The Sun enters the main sequence undergoing stable hydrogen fusion, which drives its luminosity. The notion that the Sun was dimmer early in the main sequence derives from models showing a solar core that is less dense and contains less helium. As core density increases as hydrogen is converted to helium, the resultant heating accounts for the steady brightening since.

Carl Sagan was an early voice in exploring the ‘faint young Sun’ problem in relation to liquid water and the matter is still controversial, although a number of possibilities exist. The authors believe the logical way to explain why a fainter star could provide conditions for liquid water on the surface is through the presence of greenhouse gases like methane and carbon dioxide, although the influence of methane is problematic unless, as in recent papers, scientists invoke planetary impacts or a primitive photosynthetic biosphere that amplifies the methane cycle. Whatever the case, mechanisms to regulate habitability are clearly crucial. From the chapter:

It is remarkable that Earth seems to have become habitable within its first few hundreds of millions of years and maintained that state seemingly without interruption to the present. This persistence is a testimony to the power of feedbacks that drive and regulate climate evolution with notable success on Earth in comparison with our Solar System neighbors Venus and Mars. Most important is the silicate weathering negative feedback, whereby rising temperatures coinciding with a warming Sun are offset by increasing rates of CO2 consumption through continental weathering, which is enhanced under warmer, wetter conditions. And we can thank diverse plate tectonic processes and their roles in such carbon cycling for this sustained thermostatic capacity over much of our history.

But let’s return to that very early Sun emerging onto the main sequence. Factors affecting a young star’s luminosity include the rotation rate of the star, and here we have little information (the Sun’s rotational rate in this era is uncertain, although some evidence suggests that it was a slow rotator). But the earliest planets could have been pummeled by radiation in this early state for tens or even hundreds of millions of years, which would have had a dire effect on any atmospheres they had formed. Note this:

…the intensity of the emission depends on the rotation rates of the stars, which are highly variable (from observation of stars in <500 Myr old stellar clusters). “Fast rotating” young stars can reach about a hundred times the rotation rate of the modern Sun, whereas moderate rotators could rotate at about ten times that rate and slow rotators would reach a few times the Sun’s rotation rate (Tu et al., 2015). Corresponding luminosities for young stars in the EUV and X-ray range of the spectrum can reach on the order of a 1000 times present mean solar luminosity at similar wavelengths for fast rotators, a few 100 times for moderate rotators and between a few tens to a hundred times the reference for slow rotators.

We’ve looked before at both the solar wind and solar flares as factors influencing planetary atmospheres and interacting with their magnetic fields, perhaps stripping atmospheres entirely in the case of M-class planets orbiting tightly around their primary. Atmospheric escape takes two forms, the first being thermal loss, where atoms are accelerated to the point where they reach escape velocity. Intense radiation is one but not the only way of doing this, but the effect on an atmosphere can be dire.

Other processes that can adversely affect an atmosphere include ions being accelerated along magnetic field lines by the solar wind or photochemical reactions. You would think that these effects would vary with distance from the star, but as the authors note, the loss estimates for Mars, Venus and Earth are relatively similar, and this despite the major differences in the makeup of the atmospheres on these planets and their magnetic field situation. Mars lacks a protective magnetic field today but seems to have had one in the past. Venus likewise lacks an intrinsic magnetic field like that produced on Earth through its convective dynamo, although interactions between the solar wind and the CO2-rich atmosphere do produce a weak magnetic effect.

Image: Diagramming a solar flare encountering Earth’s magnetosphere. Credit: Jing Liu (Shandong University, China and National Center for Atmospheric Research in the U.S).

As to the Sun, variations in the solar magnetic field over time are assumed given that a faster spinning star would have produced higher levels of magnetic activity. Today’s solar cycle, eleven years long, is the result of the magnetic reversal cycle of the Sun. The twists and tangles of magnetic field lines during this cycle cause sunspot activity to peak and then decline as the north and south magnetic poles reverse. The Sun’s magnetic field strengthens and weakens during the cycle, with effects apparent in the solar wind itself and in spectacular events like coronal mass ejections.

If we back out to the largest timescales, the variations in the Sun’s magnetic field indicate a much stronger field early in the Sun’s evolution, coupled with a (presumed) faster stellar rotation rate. From the standpoint of habitability, that tells us that ultraviolet and X-ray flux along with the solar wind has been decreasing with time. We’re probably talking about orders of magnitude difference in UV and X-ray radiation, but the authors point out that the intensity of emission depends upon the rotation rate of stars, and there is much we still have to learn about both this and luminosity.

The high degree of uncertainty on the Sun’s rotation rate and temperature affect our estimates of the ultraviolet at X-ray emissions our star would have produced, and thus the impact of this flux on the atmospheres of the terrestrial planets. Enlarging our field of view to exoplanets, it’s clear that the more we can piece together about the Sun’s early history, the more we can learn about the atmospheres and habitability of planets around the various spectral types of stars. Kane and team see the Sun as a template for planetary evolution, which makes heliophysics crucial for the study of astrobiology.

This study, then, homes in on the factors that need to be clarified as both heliophysics and exoplanetary science move forward. Even the closest planet to us presents formidable challenges, and the authors’ discussion of Venus is well worth your time. Here we have a world whose young surface – relatively uniform in the range of 250 to 1000 million years old – makes digging into its more remote past all the more difficult. Evidence can only be indirect at this stage of planetary exploration. We’re lucky to have Mars within reach as we widen the study of planetary formation to worlds other than our own.

The chapter in the Elsevier book is Kane et al., “Our Solar System Neighborhood: Three Diverging Tales of Planetary Habitability and Windows to Earth’s Past and Future,” available as a preprint. Two Sagan papers on the faint young Sun paradox are notable: Sagan & Mullen, “Earth and Mars: Evolution of Atmospheres and Surface Temperatures”, Science 177 (1972), 52 (abstract) and Sagan & Chyba, “The early faint sun paradox: Organic shielding of ultraviolet-labile greenhouse gases,” Science 276 (1997), 1217 (abstract). You might also want to look at Ozaki et al., “Effects of primitive photosynthesis on Earth’s early climate system,” Nature Geoscience 11 (2018), 55-59 (abstract), which offers up a methane solution for the faint young Sun.

Vega’s Puzzling Disk

Over the weekend I learned about Joseph Haydn’s Symphony No. 47, unusual in that it offers up some of its treasures in perfect symmetry. Dubbed ‘The Palindrome,’ the symphony’s third movement, Minuetto e Trio, is crafted to play identically whether attacked normally – moving forward through the score – or backwards. You can check this out for yourself in this YouTube video, or on this non-auditory reference.

The pleasure of unexpected symmetry is profound, and when seen through the eyes of our spacecraft, can be startling. Consider the storied star Vega. We see this system from our perspective at a very low inclination angle relative to its rotational axis, as if we were looking down from above the star’s pole. This face-on perspective is profoundly interesting when examined through our space-borne astronomical assets. In the image below, we get two views of Vega’s disk, from Hubble and then JWST.

Image: The disk around Vega as seen by Hubble (left) and Webb (right). Hubble detects reflected light from dust the size of smoke particles largely in a halo on the periphery of the 160-billion-kilometer-wide disk. Webb resolves the glow of warm dust in a disk halo, at 37 billion kilometers out. The outer disk (analogous to the solar system’s Kuiper Belt) extends from 11 billion kilometers to 24 billion kilometers. The inner disk extends from the inner edge of the outer disk down to close proximity to the star. Credit: NASA, ESA, CSA, STScI, S. Wolff (University of Arizona), K. Su (University of Arizona), A. Gáspár (University of Arizona).

We don’t, of course, have the perfect symmetry of the Haydn minuet and trio here, but do notice how smooth this disk appears, and particularly take note of the lack of any embedded planets, the sort of large objects we observe in formation around stars like Beta Pictoris. This bright star, a summer object in Lyra for those of us in the northern hemisphere, was well studied in the infrared by astronomers using the Spitzer Space Telescope, and now we have the clearest view ever, the subject of two upcoming papers in The Astrophysical Journal. Co-author Andras Gáspár (Steward Observatory, University of Arizona, calls the Vega disk “ridiculously smooth.”

The view shows layered structure, with Hubble detecting dust on the outer regions of the disk and Webb’s infrared view resolving the warmer dust in the inner disk, the disk in this region being sand-sized as compared to the outer halo, whose particles are of the consistency of smoke. These are useful observations because they offer information on dust movement in circumstellar disks, and also point out the stark difference among the planetary disks thus far observed. The hot, A-class Vega at 450 million years old remains a relatively young star and we would expect interactions among debris in the disk to keep replenishing it, a process that continues in our own much older system.

But where are the planets in formation? Lead author Kate Su (University of Arizona), says that the lack of them forces astronomers to rethink the way they’ve looked at forming planetary systems. It’s possible to tease out a gap at about 60 AU, but everywhere else the disk appears smooth, which rules out planets larger than Neptune in outer orbits. Adds Su:

“We’re seeing in detail how much variety there is among circumstellar disks, and how that variety is tied into the underlying planetary systems. We’re finding a lot out about the planetary systems — even when we can’t see what might be hidden planets. There’s still a lot of unknowns in the planet-formation process, and I think these new observations of Vega are going to help constrain models of planet formation.”

In the second of the two papers, lead author Schuyler Wolff (University of Arizona) and colleagues home in on the star Fomalhaut by way of comparison, this being a star that is a close twin to Vega in terms of luminosity, distance and age. As the paper notes, “[T]he Vega disk morphology differs significantly from Fomalhaut,” going on to say:

Vega’s fellow archetypical disk, Fomalhaut, has been extensively studied in scattered light (Kalas et al. 2005; Gáspár & Rieke 2020) and shows a narrow cold belt from 130-150 au (possibly confined by an undetected planet e.g., Boley et al. 2012) with a scattered light halo extending outwards from the belt. The parent planetesimal belt is clearly detected with ALMA (MacGregor et al. 2017), with an estimated dust mass of 0.015±0.010M⊕. Fomalhaut has also recently been the target of groundbreaking JWST observations (Gáspár et al. 2023) showing the same narrow cold belt (albeit with a slight radial offset indicative of grain size stratification) and halo.

Indeed, Fomalhaut appears to be building a planet within its debris disk, and possibly more than one, these objects acting as ‘shepherds’ shaping the disk. Any such worlds in the Vega system are clearly much smaller, if indeed they exist. Vega’s dust distribution is broad, whereas at Fomalhaut the outer debris ring is the dominant source of light available for our observation. Three nested debris belts appear at Fomalhaut.

Nothing better than a new astronomical puzzle, especially when it challenges our notions of planet formation. You may remember Vega’s role in Heinlein’s Have Spacesuit Will Travel (1958), where its civilization acts as a kind of overseer for Earth, and perhaps the ‘Vegan Tyranny’ from James Blish’s Cities in Flight series. For that matter, Vega has an important commercial role in Asimov (the source of ‘Vegan tobacco’ in the Foundation books), appears prominently in Jack Vance’s work, and is of course of great interest to Ellie Arroway in Carl Sagan’s book and film Contact. How enjoyable that it now throws a new mystery at us.

The papers are Su et al., “Imaging of the Vega Debris System using JWST/MIRI,” accepted at The Astrophysical Journal (preprint) and Wolff et al., “Deep Search for a scattered light dust halo around Vega with the Hubble Space Telescope,” accepted at The Astrophysical Journal (preprint).

Monkeying Around with Shakespeare

Bear with me today while I explore the pleasures of the Infinite Monkey Theorem. We’re all familiar with it: Set a monkey typing for an infinite amount of time and eventually the works of Shakespeare emerge. It’s a pleasing thought experiment because it’s so visual and involves animals that are like us in many ways. Now we learn from a new paper that the amount of time involved to reproduce the Bard is actually longer than the age of the universe. About which more in a moment, but indulge me again as I explore infinite monkeys as they appear in fictional form in the mid-20th Century.

In “Inflexible Logic,” which ran in The New Yorker‘s February 3, 1940 issue, Russell Maloney tells the tale of a man named Bainbridge, a bachelor, dilettante and wealthy New Yorker who lived in luxury in a remote part of Connecticut, “in a large old house with a carriage drive, a conservatory, a tennis court, and a well-selected library.” He has about him the air of an English country gentlemen of the 18th Century, interested in both the arts and science. An eccentric.

One night at a party in the city, Bainbridge enters into conversation with literary critic Bernard Weiss, who he overhears saying of a lionized author: “Of course he wrote one good novel. It’s not surprising. After all, we know that if six chimpanzees were set to work pounding six typewriters at random, they would, in a million years, write all the books in the British Museum.”

Impressed, Bainbridge learns that the experiment has never been tried. He acquires six chimpanzees and provides them with paper and typewriters. Some weeks later, he is with James Mallard, an assistant professor of mathematics at Yale, whom he has asked to his estate to discuss the ongoing experiment. Showing him the monkeys at work, he points to tall piles of manuscript along the wall, containing in each complete works by writers such as Charles Dickens, Anatole France, Somerset Maugham and Marcel Proust.

Image credit: Amazingly generated by Gemini AI. Note that the three foreground monkeys have their typewriters facing the wrong way, but I suppose it doesn’t matter, as they can still reach the keys.

Indeed, since the beginning of the experiment over a month before, not a single monkey has spoiled a single sheet of paper. Great literary works continue to pile up. After Mallard leaves, the weeks go by and the monkeys never cease their labors. They produce Trevelyan’s Life of Macaulay, The Confessions of St. Augustine, Vanity Fair and more. Bainbridge keeps passing this information on to Mallard, who grows increasingly confounded. And worried.

Finally, when leafing through a manuscript of Pepys’ Diary produced by Chimpanzee F (named Corky), a work that contains material not in his own abridged edition, Bainbridge is again visited by Mallard at his home. Taken back to the scene of the experiment, Mallard pulls out two revolvers and shoots the chimpanzees. Both men end up, after a fight, shooting each other and both die. Mallard’s last words: “The human equation…always the enemy of science… I deserve a Nobel.”

And so the story concludes:

“When the old butler came running into the conservatory to investigate the noises, his eyes were met by a truly appalling sight. A newly risen moon shone in through the conservatory windows on the corpses of the two gentlemen, each clutching a smoking revolver. Five of the chimpanzees were dead. The sixth was Chimpanzee I. His right arm disabled, obviously bleeding to death, he was slumped before his typewriter. Painfully, with his left hand, he took from the machine the completed last page of Florio’s Montaigne. Groping for a fresh sheet, he inserted it, and typed with one finger, “UNCLE TOM’S CABIN, by Harriett Beecher Stowe. Chapte…” Then he too was dead.”

Maloney was a Harvard grad who seeded ideas for many of The New Yorker‘s cartoons; he became editor and writer of the Talk of the Town section. Here he shows us what happens when something absurd becomes true. The story was reprinted in Clifton Fadiman’s Fantasia Mathematica (Simon and Schuster, 1958).

What would actually happen if we set up Bainbridge’s test? The new work exploring this is out of the University of Sydney, where Stephen Woodcock and Jay Falletta considered the problem within a more spacious context. Bainbridge was dealing with a tiny cadre of six monkeys. But most versions of the thought experiment involve infinity. Woodcock explains:

“The Infinite Monkey Theorem only considers the infinite limit, with either an infinite number of monkeys or an infinite time period of monkey labour. We decided to look at the probability of a given string of letters being typed by a finite number of monkeys within a finite time period consistent with estimates for the lifespan of our universe.”

This is the kind of thing mathematicians do, and I have often wished I had the slightest gift for math so I could join the company of such a jolly group. Or maybe that’s only in Australia, because I’ve known a few grim mathematicians as well. Whatever the case, the new paper appears in a peer-reviewed journal called Franklin Open. The authors assume a keyboard with 30 keys, which allows for all the letters of English along with the most common of the punctuation marks. They assumed that one key would be pressed every second until the end of the universe in 10100 years.

The latter are bold assumptions considering monkey finger dexterity as well as attention span, and I’ll also note that the end of universe calculation is very much up for grabs, although excellent books like Fred Adams and Greg Laughlin’s The Five Ages of the Universe deal with numbers like this. Still, we’re not exactly sure that the accelerating expansion of the universe is stable, or what it might do one day.

But enough of that.

Get this: There is a 5% chance that a single chimpanzee might type the word ‘bananas’ in its lifetime. But Woodcock and Falletta worked out two sets calculations, the second involving a population of 200,000 chimpanzees (200,000 is apparently the current global population of chimpanzees, although that number seems low to me). Anyway, if you throw the entire 200,000-strong retinue at Shakespeare, the Bard’s 884,647 words will not be typed before the end of the universe. As the authors point out:

“It is not plausible that, even with improved typing speeds or an increase in chimpanzee populations, monkey labour will ever be a viable tool for developing non-trivial written works.”

AI is another matter…

Of course, Mr. Bainbridge used only six monkeys, and look what he got. I think we can take the ending of the Russell Maloney story to be saying something about our attitudes toward science. Our essential understanding of probability had better be right. If it turns out we unleash monkeys who begin typing out For Whom the Bell Tolls, we are confronted with not just an improbability, but an assault on the structure of the cosmos. We can see why professor Mallard lost his wits and blew the monkeys away, an outcome that, had the story been written in our more animal-considerate times, would not have been allowed by the editor.

Mallard thought an impossibility could not be allowed to exist. He had saved science.

And I have to add the delightful conclusion from the paper:

Given plausible estimates of the lifespan of the universe and the amount of possible monkey typists available, this still leaves huge orders of magnitude differences between the resources available and those required for non-trivial text generation. As such, we have to conclude that Shakespeare himself inadvertently provided the answer as to whether monkey labour could meaningfully be a replacement for human endeavour as a source of scholarship or creativity. To quote Hamlet, Act 3, Scene 3, Line 87: “No”.

The paper is Woodcock and Falletta, “A Numerical Evaluation of the Finite Monkeys Theorem,” Franklin Open Vol. 9 (December, 2024) 100171 (full text).

Deep Space Implications for CubeSats

The Hera mission has been dwarfed in press coverage by the recent SpaceX Starship booster retrieval and the launch of Europa Clipper, both successful and significant. But let’s not ignore Hera. Its game plan is to check on the asteroid Dimorphos, which became the first body in the Solar System to have its orbit altered by human technologies when the DART spacecraft impacted it in 2022. Hera is all about assessing this double asteroid system to see first-hand the consequences of the impact, which shortened the smaller object’s orbit around asteroid Didymos by some 32 minutes.

That’s a pretty good result, some 25 times what NASA had defined as the minimum successful orbital period change, and we’re learning more about the ejecta, which involve tons of asteroidal rock. The collision occurred at 6.1 kilometers per second, to be more fully assessed by Hera’s twin CubeSat craft, which will make precise measurements of Dimorphos’ mass to analyze the efficiency of the impact. All this factors into planning for asteroid impact missions if an object ever threatens Earth.

Image: Astronomers using the NSF’s NOIRLab’s SOAR telescope in Chile captured the vast plume of dust and debris blasted from the surface of the asteroid Dimorphos by NASA’s DART spacecraft when it impacted on 26 September 2022. In this image, the more than 10,000 kilometer long dust trail — the ejecta that has been pushed away by the Sun’s radiation pressure, not unlike the tail of a comet — can be seen stretching from the center to the right-hand edge of the field of view. Credit: CTIO/NOIRLab/SOAR/NSF/AURA/T. Kareta (Lowell Observatory), M. Knight (US Naval Academy).

I want to draw your attention to those two CubeSats aboard Hera. My thinking is that these miniature spacecraft, built upon standardized 10-cm boxes, are a story as big as the results they’ll gather. There are two of them: Juventas is the product of GOMspace (Luxembourg), designed to make the first radar probe of the interior of an asteroid. Milani was produced by Tyvak International, an Italian operation. Its job is to perform multispectral mineral prospecting. Their recent activation for a check of on-board systems was in both cases completely successful. Says ESA engineer Franco Perez Lissi:

“Each CubeSat was activated for about an hour in turn, in live sessions with the ground to perform commissioning – what we call ‘are you alive?’ and ‘stowed checkout’ tests. The pair are currently stowed within their Deep Space Deployers, but we were able to activate every onboard system in turn, including their platform avionics, instruments and the inter-satellite links they will use to talk to Hera, as well as spinning up and down their reaction wheels which will be employed for attitude control.”

So this is good news for the Hera mission, but in the larger context we are seeing the continuing growth of miniaturized technologies that will improve the efficiency and capability of missions to much more distant targets. Juventas was activated on October 17 at a distance of 4 million kilometers from Earth; Milani’s turn came on October 24, with the craft 7.9 million kilometers out. Both will be deployed from their ‘mothership’ to make close approaches to Dimorphos upon arrival in 2026.

It was back in 2011 that NanoSail-D2 demonstrated successful sail deployment, to be followed by The Planetary Society’s LightSail-a in 2015. We were learning that a spacecraft as small as a CubeSat could carry a solar sail, leading to The Planetary Society’s subsequent LightSail missions. Sara Seager at MIT has investigated CubeSats as exoplanet research platforms, the notion being that a fleet of CubeSats could be deployed with each monitoring a single star. The first detection of an exoplanet by a CubeSat occurred in 2017 with the ASTERIA (Arcsecond Space Telescope Enabling Research In Astrophysics) 6U CubeSat space telescope.

NASA’s Mars Cube One (MarCO) CubeSats demonstrated multiple CubeSat operations beyond Earth orbit in 2018, and there have been a host of CubeSat projects in the hands of private companies and universities ranging from 2009’s AeroCube-3 to LunaH-Map in 2022, the latter aimed at mapping the distribution of hydrogen at the Moon’s south pole. QubeSat is a project out of UC-Berkeley to study quantum gyroscopes in low Earth orbit and explore precision control for small satellite navigation. CubeSats are cheap. Lose one at launch – and early failures abound, as witness Lunar Flashlight – and the impact on your budget is minimized.

Image: The first image captured by one of NASA’s Mars Cube One (MarCO) CubeSats. The image, which shows both the CubeSat’s unfolded high-gain antenna at right and the Earth and its moon in the center, was acquired by MarCO-B on May 9, 2018. Credit: NASA/JPL-Caltech.

Most CubeSat missions have been designed for low-Earth orbit but some scientists are aiming to go much farther. In a 2023 paper Slava Turyshev (JPL) and colleagues investigated small spacecraft (smallsats) with solar sails in missions to the outer system. In general, a ‘smallsat’ refers to a spacecraft that is both small and lightweight, usually less than 500 kilograms, and sometimes much less, as when we get into the realm of CubeSats.

Smallsats with solar sails are a combination of miniaturization and efficiency, for a sail requires no on-board propellant and can be sent on ‘sundiver’ trajectories that could achieve, in the view of the authors, velocities of 33 kilometers per second (7 AU per year). By comparison, Voyager 1’s pace is 17.1 kilometers per second. Using chemical propulsion, we would need 15 years to reach Uranus, so much faster travel times are welcome.

So let’s add to Sara Seager’s ideas on exoplanet constellations of CubeSats the idea of solar sail smallsats on fast trajectories for flyby missions, impactor missions like DART, and formation and swarm operations at targets like the ice giants, about which we know all too little. The challenge here will be the need for lightweight instrumentation and continuing miniaturization, both trends that seem to be accelerating. Two-years to Jupiter and three to Saturn at these velocities are tantalizing prospects as Turyshev and team continue to study sailcraft designs to reach the Sun’s gravity lens beginning at 550 AU.

How does a fleet of future smallsats hardened for deep space and using modularized components stack up against, say, a single enormous (by comparison) orbiter to Uranus or Neptune? The two could, of course, work together, but given the costs, flyby missions on the cheap in their tens or hundreds could offer priceless scientific return. We always return to the practicalities of prying money out of political entities, so finding ways to lighten the budget while accomplishing the mission will continue to be a priority. Will we see an ice giant orbiter off in the 2030s? Somehow I doubt it.

The exoplanet paper via CubeSat constellation mentioned above is “Demonstrating high-precision photometry with a CubeSat: ASTERIA observations of 55 Cancri e,” The Astronomical Journal Vol. 160, No. 1 (2020), 23 (full text). The Turyshev paper is “Science opportunities with solar sailing smallsats,” Planetary and Space Science Vol. 235 (1 October 2023). Full text. For more on all this, see Building Smallsat Capabilities for the Outer System, published last year in these pages.

Charter

In Centauri Dreams, Paul Gilster looks at peer-reviewed research on deep space exploration, with an eye toward interstellar possibilities. For many years this site coordinated its efforts with the Tau Zero Foundation. It now serves as an independent forum for deep space news and ideas. In the logo above, the leftmost star is Alpha Centauri, a triple system closer than any other star, and a primary target for early interstellar probes. To its right is Beta Centauri (not a part of the Alpha Centauri system), with Beta, Gamma, Delta and Epsilon Crucis, stars in the Southern Cross, visible at the far right (image courtesy of Marco Lorenzi).

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