Stepstones to infinity

 kw: book reviews, nonfiction, science, astronomy, space science, popular treatments

My favorite astrophysicist, Neil deGrasse Tyson, published a new book last year in collaboration with Lindsey Nyx Walker, in the Startalk series: To Infinity and Beyond: A Journey of Cosmic Discovery. With apologies to Buzz Lightyear, the title makes it clear this is no scientific treatise.

As one might expect, the book is fun to read, pitched at just the right level for a popular audience, and copiously illustrated. Rather than chapters, the book has four sections, with a subtitle every couple of pages. The sections are titled "Leaving Earth", "Touring the Sun's Backyard", "Into Outer Space", and "To Infinity and Beyond". Broadly speaking, the sections are like layers of an onion, starting at the center.

The second section, on the planets and their satellites and asteroids and other denizens of the solar system, is the longest, as befits the greater knowledge we have "in the Sun's back yard", where at least we have sent instruments to pass by or even orbit the planets and selected objects. The book went to press before the capsule of material returned from Asteroid Bennu was opened, so that's not mentioned. What is mentioned is the quest to colonize Mars, which cannot realistically be done without terraforming it. Engineering solutions, including carpet bombing the polar ice caps with nuclear weapons, have been proposed. Dr. Tyson has this to say:

"In any case, if humanity ever develops enough geoengineering know-how to terraform Mars as our escape plan after we trash Earth, then we should certainly be able to use that intelligence to make Earth livable again and save ourselves from requiring a planet B in the first place." (p. 135)

To which I add a strong, "Amen!"

The fourth section, after treating what we know of the distant cosmos in a general way, gets a bit philosophical. The authors have this to say about "beyond", that is, about the many-worlds interpretation of quantum uncertainty: "The many-worlds solution may not be simple, but it is the simplest explanation for the oddities at quantum scales." I must contend with that:

Consider sunlight shining through an ordinary window. When the light encounters the glass, ~4% is reflected from the outer surface and ~96% passes into the glass. Then about another 4% is reflected from the second surface and the rest, ~92%, continues onward. Interestingly, the light that reflected back into the glass pane is partly reflected and then most passes through. Some smaller and smaller fraction of the original light bounces back and forth inside the glass pane. Glass is not 100% transparent, to soon whatever has not escaped is absorbed. Considering only visible light, sunlight has an intensity of around 500 watts per square meter, or 0.05 watt (50 mw) per square centimeter. Skipping the math, the number of photons of visible light that encounter the glass each second is about 1.4x10¹⁷, or 140 quadrillion (140 million billion). Each photon "decides" whether to reflect or pass through, twice because the glass has two surfaces. According to the many-worlds interpretation, 280 quadrillion entire universes are created every second, because of sunlight shining through one square centimeter of glass. I have a picture window in my family room that has an area of two square meters. On a sunny morning, every second, about 5.6x10²¹ universes spring into existence, along what dimensions we have know way to discern. Five and a half sextillion. Every second.

Folks, that's just silly. Whatever photons and other quanta are, they are doing something we fundamentally don't understand, and interpretations such as many-worlds reveal how immensely far we are from achieving such understanding.

We are like the pilgrim in this famous engraving from an 1888 book by Flammarion, trying to see beyond our own horizon. Our imagination falls short. Newton imagined himself as a beach comber being fascinated by this shell or that pretty pebble, being ignorant of the expanse of the ocean that tossed them up.

All that aside, and aside from a few errata I'll get into shortly, the book is as entertaining as it is comprehensive. I strongly recommend it.

---------------------------

I have to bring out a few matters where the authors, or a copy editor, ought to have known better:

1. On p. 22, about warming by infrared light, "…once they absorb the various wavelengths of radiation, molecules on Earth's surface are transformed into infrared and are reemitted by the ground." This is a rather dramatic blunder. The molecules are not transformed into infrared! The relevant phrase should read, "…molecules on Earth's surface emit infrared radiation." All the wavelengths of sunlight that reach the ground warm its substance, and it then emits some of this energy as infrared.
2. On p. 119, about the slowing of Earth's rotation, mostly by its interaction with the Moon, it is stated, "After two centuries, days are four milliseconds faster." In this context, the word "faster" is misused. The days are "four milliseconds longer." Gah!
3. On p. 131, "Today, Mars is a frigid tundra." The word "tundra" implies a cold landscape with cold-resistant plant cover. There are no plants on Mars. I don't know what word to use, but the word "tundra" is wrong.
4. On p. 206, on relationships between the intrinsic brightness of stars and their apparent brightness because of their varying distances, "Sirius, the brightest star in our night sky, is smaller than Earth and 8.6 light-years away,…" Siriusly?!?!? As it happens, Sirius is 1.7 times the size of the Sun. Its companion, the white dwarf designated Sirius B, which is much too faint to see without a large telescope, is indeed smaller than Earth.
5. Finally, look carefully at this illustration of a prism producing a spectrum:

This is found on p. 212, where spectroscopy is being discussed. The illustration is from Getty Images. The way the beam of light bends upward as it enters the prism implies that the prism has a refractive index less than 1, which is impossible. Such a material would require the light to go "faster than light" within it.

Compare with this illustration:

This is from Britannica online. It is more correct, showing the light entering being refracted toward the perpendicular to the glass surface as it passes into the prism, and then refracted away from the perpendicular of the second glass surface as it exits. P.S. I was a spectroscopist for a few years…

This illustration isn't totally accurate, however. The best spectroscopic glass disperses the spectrum by a little less than one degree. The spectrum at the right is being dispersed about 15°. However, this bit of scientific license is needed to make the principle more clear.

I put the query "prism spectrum" into a Google Images search. I found that a great many repositories of stock photos have it wrong; only about one-third have it right! Don't Getty and all the others have anyone with scientific understanding on their staffs?

Getting a direct look

kw: astronomy, space science, extrasolar planets, stars

As a pre-requisite to some of the discussion below, it would be a good idea to read this Stellar Classification article.

The Kepler mission to discover earth-like extrasolar planets has been under weigh for most of a year. It occurred to me to do a calculation or two to see what they are up against. This space mission uses a telescope, a smaller version of the Hubble telescope, to look at thousands of stars, searching for planetary eclipses.

Among the questions you want to answer when planning such a mission are

• What kind of star to watch
• How sensitive the detector needs to be
• How frequently each star needs to be checked
• How many stars to watch

There are others, but these are the biggest factors.

What kind of star to watch? The star classification is most important, because it determines how long the star will stably warm a planet without melting it. The sun is a G type star, specifically G2. From heaviest to lightest, and along the Main Sequence (the portion of a star's existence that it is relatively stable), stars are classified O B A F G K M. Heavy stars are rare but very bright, so we see lots of O, B and A stars in the night sky. Light stars, lighter than the Sun, are very abundant but less luminous, so not many such stars are visible to the naked eye. The brightest G type star is the famous Alpha Centauri double star, visible from the southern hemisphere, which is of the first magnitude, appearing about one-tenth the brightness of Sirius, the brightest. It is only 4.4 light years away, so it can be that visible. About a tenth of the total brightness is supplied by Beta Centauri, a K type star that is so close it takes a telescope to distinguish them.

The Sun is a young-to-middle-aged star, just 4.5 billion years old. It has steadily warmed, now being 40% brighter than it was 4 billion years ago. It will continue to do so, and the Earth will become too hot for life in about half a billion to one billion years. So a G2 star can keep a planet habitable for about five billion years. That has been long enough for complex life to arise in this case, but whether this is common or very rare, we're trying to find out (the Kepler mission is part of the effort).

Let's consider a star that is one-quarter as bright as the Sun. Its classification would be K2 or K3. Its mass would be about 0.7 the Sun's, which means its expected stable existence would be about three times as long. It is a good candidate for hosting a life-bearing planet. The planet is also far enough from the star that it won't be tidally locked, which is considered a detriment.

If we were to consider heavier, brighter, hotter stars than the sun, their "useful lifetime" is shorter. Unless life gets going quickly, and complex life is correspondingly "easy", there is little chance for an A or F star to host aliens we could talk to.

Of all Main Sequence stars, G stars comprise 7.5% and K stars comprise 12%. What about M stars? They are all quite a bit dimmer than the Sun, 8% or less of total energy released. While they have spectacular terms of existence (many billions to trillions of years), most are somewhat unstable, the more so as you go from M1 to M9. Many are flare stars and would periodically sterilize any planet in the otherwise "habitable zone". Some M stars may be suitable hosts for life-bearing planets, but even though M stars in total comprise 75% of all stars, few of these are that suitable. So the focus of a mission like Kepler is on G and K stars. Of the seven exoplanets so far found by Kepler (all of them too hot, but a good test of the system) all were found orbiting stars a bit larger than the Sun. Detector sensitivity is part of the story.

How sensitive a detector? The primary issue here is strong linearity and discrimination. When Earth crosses in front of the Sun, it blocks only 0.000084 of the light, a factor of 1/11,800. You need to be able to "see" such a difference clearly. That means each observation must be long enough to gather plenty of photons so statistical noise is much smaller than the signal. Photon statistics follow a Poisson distribution, which has a standard deviation (SD) of the square root of the mean. Gather one million photons, and your scatter is 99% confined to three SD units, or plus/minus three thousand. That is a third of a percent. Go for ten billion: the scatter in readings will be 300,000 counts, or one in 33,333. That is a good level to shoot for.

This has two implications. One is, you need to return to each star you are watching about hourly. If you are watching 3,600 stars, each one gets about one second of photon-gathering time. Of course, the light is being gathered by a large imaging detector, so you can gather many stars' data at once. In the ideal case, the telescope can be pointed to a single area and watch it for up to a year, gathering thousands of millions of stars' light curves almost continuously. But to gather ten billion photons per star, you need an integration time of sufficient length, which could be from a few minutes to an hour, depending on the brightness of the star.

That is the second consideration. Brighter stars can be usefully measured from farther away, but it is the dimmer stars in which we are most interested. This tradeoff also steers our search parameters in the direction of G stars and the brighter half of K series stars. Only a small number of M stars are close enough.

How frequently to check each star? This boils down to, how long does an eclipse last? If someone is watching us with their own Kepler mission, and they are located right on the ecliptic, they will see a 13-hour eclipse each Earth year. For the K3 star described earlier, the longest possible eclipse is 11.5 hours, but it occurs almost twice as frequently. Back to Earth eclipses of Sol: If the earth is viewed such that it is 0.997 of the Sun's radius from a central eclipse, the eclipse will last just one hour. That is near the detection limit, for the Earth will stay in the region of limb darkening, and darken the Sun my a factor closer to 1/20,000.

This means that the longest time lag between observations should be of the order of an hour. A few minutes is better, but this depends on the brightness of the star and the number of photons our telescope gathers for it.

How many stars to watch? How many Earths do there need to be for a single observer to observe just one of them? The geometry works out to 338. Put another way, only one in 338 stars in the heavens is situated close enough to the ecliptic to detect Earth using the eclipse method. For the K3 star? the figure is 200, because the planet is closer to the star. This means the Kepler mission is more likely to find planets in the habitable zone of K stars than for G stars. If you want to find one hundred Earths, you need to observe twenty or thirty thousand stars.

That is close to the stated goal of Kepler's mission, with one caveat: Not all stars are expected to have planets in "Goldilocks" orbits, not too close, not too far, but just right. Some consider that only 5-10% of the target stars actually have the right kind of planet. Some consider it is closer to 50%. By watching 100,000 stars, we have a pretty good chance to refine this number, at the very least.

A few years from now, we ought to have much better statistics on just how many planets there are in the Galaxy that could harbor life. Then it is up to the engineers to put something in orbit with sufficient data-gathering power (a big mirror!, or 2-3 of them) to look for oxygen in a planet's atmosphere, or other signs of life, while fending off the parent star's glare.

My meteorwrong

kw: information, space science, meteorites

Proving myself wrong about a rock

I've carried this rock around for so many years I've forgotten where I found it. I suspect, though, it was on a trip to San Benito County, California, with a group of fellow Geology students looking at the ultramafic rocks there.

"Ultramafic" refers to rocks with high Magnesium and Iron content; the County is host to a sequence of rocks derived from the upper part of the Mantle during a continental collision.

The connection of this rock with that trip is only in retrospect. Since finding the rock in a box several years ago, I've considered it might be a meteorite, mainly because it is rather heavy and sort of "looks right". Recently I decided to find out.

I decided to first measure its density. I don't have lab equipment available, so I used what I found in the kitchen: a spice scale (capacity 0.5kg) and a 0.5 liter measuring cup. I weighed the stone (210g), then put the stone in the cup and added water until it was covered, turned it all ways with a spoon to knock off all bubbles, then topped it to 500cc, the top line on the cup. I fished out the stone and read "a little below 450", which I estimated as just above 440cc. So the difference was less than 60cc, and I called it 58-to-60cc. Divide these limits into 210, and the result is 3.5-3.6 g/cc. That's in the right range for a stony-iron meteorite.

Checking relative accuracy, I decided I wasn't quite satisfied. The scale is marked each 10g, and can be read to 5g with care, so 210±5 meant a range of ±2.3%. The measuring cup, however, is only marked each 50cc, and it is hard to read a fifth of a marking, particularly because their spacing changes on the tapered cup. Generously assuming I can read to 10cc accurately, I still was faced with a range of ±10cc out of about sixty, or about ±17%. And there's no telling how properly printed the markings are...

So I used weight instead of volume. I tied a thread harness to the rock, so it would hang flat. I put the rock into the cup with enough water to cover it when I lifted it clear of the bottom. The whole rig exceeded the capacity of the scale, but not when I lifted the rock above the bottom of the cup, yet still under the water. I could just make it: 490 grams. Then I lifted the rock all the way out, and the reading dropped to, as nearly as I could tell, between 435cc and 440cc. I split the difference at 52.5±2.5cc, an error figure of ±4.8%. Now we're getting somewhere.

The result was 4.0g/cc, ±5.3%, or a range from 3.8-4.2. The former measurement, 3.55 with a ±17% range, covers a possible span of 2.9-4.2! Anyway, it doesn't contradict the new measurement. Now...what has a density of 4?

Stony meteorites have a density in the range 3.0-3.3. Iron ones are near 8, and even stony-iron ones are typically less than 3.8. My stone is either too heavy or too light to be a meteorite, and is not magnetic, so stony-iron is out. A closer look provides a further clue.

This broken surface, which is in the shadow to the left of the first photo, shows holes inside the rock.

A quick look at the Meteorite Realities page confirmed my suspicion that no meteorite formed with internal holes; there is no gas in space to open the holes, and these are clearly gas bubble holes. Though they appear to constitute only a few percent of the rock, they indicate that the bulk density without porosity ought to be several percent greater, at least 4.2-4.4 g/c. Now I'm in trouble...

The rounded lump at the arrow is reddish compared to the solidly gray background. Is it a garnet? Perhaps the garnet (or whatever) is one of the denser types, but it has to constitute most of the rock to have much effect. The usual sort of garnet peridotite seldom exceeds a density of 3.5, and this rock isn't green enough to be a peridotite (think the black sands of Hawaii, which are really blackish green, formed of peridot sand).

This image, around the end of the stone from the other two views, shows a squarish, reddish crystal (see the arrow). Maybe a garnet, or possibly a spinel. The reddish stain below gave me another clue, and there are several around the stone (see the first image). Now I remembered that trip to San Benito. I still don't know if that is where I got the rock, because we also visited a number of mines on that trip and later ones during my Senior year as a Geology student.

What is clear is that this is a combination of garnet or spinel in a siderite-hematite mix. These occur together in metamorphic assemblages, and both San Benito County and other places I frequented in those years were metamorphic terranes with plenty of sources for iron ore, which is just what this is.

Aliens everywhere? Pack your microscope...

kw: book reviews, nonfiction, science, astrobiology, space science

Peter Ward and his colleague Don Brownlee made a host of constituencies mad when they published Rare Earth four years ago. Their conclusion is that, while life in the form of microbes may be rather common throughout the Universe, complex animal life, however constituted, the kind of life that makes cities and spaceships and radio signals, is probably exceedingly rare. Read Rare Earth for a thorough, and thorougly entertaining, study of the requirements of complex life.

Agree or disagree, you'll find they raise questions that need to be discussed even as we imagine a universe like that of Star Wars or Star Trek. My own conclusion is that this portion of the Galaxy has only recently begun to produce civilizations: Stars formed (in this region of the Galaxy) prior to our Sun have too few heavier materials with which to form rocky planets such as Earth, large enough to hold an ocean for five or ten billion years.

Also, stars formed only 1-2 billion years ago have larger amounts of rocky material, but even a larger proportion of heavy metals and radioactive materials; they are likely to form super-earths that hold too much water (no continents), and stay hotter longer. So there is a window of opportunity, which may be rather narrow, maybe not. I think we are on its leading edge.

OK, with that out of the way, I say, "Who better than Peter Ward to discuss the various kinds of life that may arise, both here and elsewhere?" Complex life of any kind may be rare...or not. But life analogous to bacteria and viruses is likely to be found nearly everywhere. In his new book, Life As We Do Not Know It, Dr. Ward warns that it may be hard to recognize as life.

His opening example is telling. When subsea hydrothermal vents were first found, there was a lot of thin, snotlike material floating around. It got in the way of observations of the big clams, crabs, and tube worms. The scientists often had to move around or wait for the water to clear so they could get nice looking photos. It was quite a while before anybody thought to capture some of the slime and look at it. It turned out to be bacterial life, in a profusion that probably outweighs the nice clams and worms. It happens to be their food, too!

It seems ludicrous. Any grazing or browsing animal weighs less than the biomass of forage needed to sustain its life. So what did they think the clams and tube worms were eating? But this is just the problem. We don't really know the limits of earthly life, in terms of temperature, pressure, or chemistry.

If you take a pinch of soil from your yard, and spread bits of it onto petri dishes containing the ten or so common nutrient mixes you can get from places like Cuisenaire or Cole-Parmer or Ward, you'll get dozens or hundreds of bacterial colonies, and if you're lucky, perhaps twenty or thirty different species. If instead, you shake that same soil sample with water, then screen for the portion smaller than two microns. Pulverize and use genetic probes, you'll find evidence that there were tens of thousands (or even millions) of different species present.

Here, this'll blow your mind: Ordinary ocean water, whether sampled shallow or deep, contains three or four parts per billion of viruses. Doesn't sound like much...it comes to 20 to 50 million virus particles per cc! Not only that, but almost every living thing on the planet contains a ppb or so of viruses, including you our me. I we had a kind of light that "saw" only viruses, the entire biosphere and all bodies of water would be outlined in a ghostly filigree of viruses, down to its last detail.

To jump to the chase, the author presents his reasons for considering viruses as living beings. Though they require living cells to reproduce, there are many species of animal parasites whose biochemistry is defective such that they cannot live outside their host.

Just to make you feel secure: the vast majority of animal species are parasites. Even though some, such as the follicle mites that live in the forehead hair follicles of at least 95% of us, are called "commensal" because they don't seem to do harm (How they might benefit us is totally unknown. Any benefit is strictly one-way, so I call them parasites).

What is life? We need enough of a definition that we'll recognize it...we just can't fall back on "I'll know it when I see it." My own formulation: "Life is a process that results when aperiodic crystals grow in an environment strongly out of equilibrium". Dr. Ward proposes, "Life metabolizes, life replicates, life evolves." Simple and functional, and more testable. It doesn't depend on a particular kind of genetic mechanism or "bio"chemistry.

What kinds of non-Earth life might we find, somewhere (even on Earth)? The author proposes Terroan to designate "life as we know it", so we can then distinguish as alien, "life as we do not know it." Terroan life is composed of cells with a lipid cell membrane, is based on Carbon, Hydrogen, Oxygen, and Nitrogen (CHON), employs water as the main solvent, and uses DNA to encode and RNA to translate genetic codes to proteins via the Universal Genetic Code (UGC). In order of increasing "alienness", we might list

• Certain bacteria that slightly violate the UGC. For example, some mycoplasmas use one of the "stop" codes (the U-G-A sequence) to encode for tryptophan.
• The parent organism of our Mitochondria; these organelles have their own, somewhat different, genetic code and reproduce independently.
• Organisms using one of the approximately 10⁷⁵ other UGCs that might be devised, though only about 10⁵⁰ of them keep redundant codes in groups. The mycoplasmas mentioned above could be included here also.
• Viruses, which are non-cellular.
• Organisms that use a solvent other than water, such as methane or a strong ammonia/water solution at very low temperatures, or hydrogen sulfate (sulfuric acid if excess water is present) at high temperatures.
• Organisms that use a polymer other than DNA to encode its genetics. (Note that silicate rocks consist of Si-O and Si-Al-O polymers. Feldspar life?)

I can think of one attribute that might make really alien life hard to recognize. Velocity. Let's look at plants. How do you tell the difference between a living and freshly-dead slice of Oak leaf? Oak trees are proverbially slow growing, though they grow leaves quickly enough each Spring. Within the cells of the leaf, though, under the microscope you can see cytoplasmic streaming going on. The insides of a cell seem to revolve complete every two or three seconds, in spite of the fact that it is encased in a porous cellulose box. Loose cells from the inside of your cheek also show streaming as long as Oxygen is present, though it is slower.

Both animals and plants of Terroan life exhibit at some scale, motions that can be observed directly by our 20-frames-per-second visual systems. That is anything from a speed just faster than the minute hand on a wall clock to velocities that blur like a spinning figure skater. But suppose we find objects in an environment whose kinematics disallow motions of such rapidity, or that are composed of much stiffer material?

A science fiction story I read was about an odd rock in an astronaut's collection, kept in a terrarium with other rock specimens from the apparently desert planet he'd visited. Every week or so, it seemed this rock had moved a little. Finally, after setting up a time-lapse camera, he was able to see that, over a few months, the odd rock moved away from the more lighted part of the terrarium, then moved to the glass side and began slowly (very slowly) grinding at it, seemingly in an attempt to escape. Perhaps it "lived" on a time scale that to it, seemed like running to a barrier and grinding through in the space of a few moments. I wonder what the astronaut seemed like from its viewpoint?

We know, kinematically, living creatures that live ten or a hundred times faster are implausible. But there is no limit to how slow one may go.

There is a point to the book. We need to expand the "tree of life" to include viruses and RNA life, at the very least, so as to include all Earth-originated and/or -developed life. We think RNA life is extinct, if it originated at all. But it may be created soon in the laboratory. Bacteria with added DNA codes have been created in the laboratory, so they are aliens. Mars probably once hosted living creatures, at least bacteria or something similar; and it may do so today, some distance below ground. Europa might have life, though the energetics are forbidding. Titan seems to have a "just right" mix of energetics and complex chemistry, that life of some kind is likely.

Thus, Dr. Ward proposes that we send people to Mars and to Titan, to look for it. Because of the differing probable history, and the known differences today, a Paleontologist needs to go to Mars and a Biochemist to Titan (better, more than one of each!). Mars is likely to have fossils, and a Paleontologist by definition is good at finding fossils. Titan doesn't seem to have anywhere on its surface that could contain fossils, but is likely to have a strong chemical signature of life processes in many places. Just what a Biochemist is prepared to determine.

You know, that's a pair of really good ideas. I hope we do it. The biggest hurdle? We have to get used to the idea that a Saturn/Titan mission is definitely one-way. Radiation there is less than near Jupiter, but still deadly over the span of a few months at most (Jupiter orbit is a DOA environment at any arrival speed less than 0.1c). Mars is probably one-way also. Can we afford to send heavy digging equipment to Mars, so astronauts can get dug in before they die of radiation poisoning? Just getting there, the DNA in 1/3 of the body cells gets damaged per year of exposure to the interplanetary environment. You gotta get a hole dug first (10m deep at least), then go there fast. Then, there is a chance to return. Send a backhoe to Mars first!

Though I was a bit put off by Rare Earth, I understand the reasoning. I find Life As We Do Not Know It much more optimistic.