Profundis: The Man Who Knew Infinity

For a long time now I’ve hoped that someone would do a movie on the life of the remarkable Indian mathematician Srinivasa Ramanujan. His story is a compelling and tragic one: born in India in the late 19th century, he began to distinguish himself as truly exceptional by the time he’d hit puberty. He worked on mathematics in isolation throughout his life, producing startling results and eventually making contact with G.H. Hardy of Cambridge University.

Hardy recognized the calibre of Ramanujan’s genius, and invited him to England. The two men had conflicting styles; Ramanujan grasped everything intuitively, often simply stating results with little to no justification, whereas Hardy was rigorous and believed strongly in proving each step. But as the First World War began and played out in Europe their productive five-year collaboration resulted in Ramanujan getting published, being elected to the London Mathematical Society and the Royal Society, and being made a Fellow of Trinity College.

Unfortunately illness was almost as consistent a theme in Ramanujan’s life as was mathematics. The diet and weather of England did not agree with him, and as his various health problems worsened he eventually decided to return to India to be with his wife and family. After spending barely a year at home, he died in 1920. He was just 32 years old.

Getting a handle on Ramanujan’s intellect necessitates some re-calibration. The chances are good that if you’re reading these words you possess a brain that is comfortably above average intelligence. Some of my readers might even be bona fide geniuses, with IQs in excess of 140 and multiple degrees to their name. They are likely unaccustomed to encountering subjects that baffle them, and have probably only met a handful of minds better than theirs.

Ramanujan makes nearly everyone look like a knuckle-dragging monkey that keeps putting its diapers on wrong. The usual descriptive vocabulary falls short here; one must reach for words like “incandescent” to do him justice.

It is this task which 2015’s “The Man Who Knew Infinity” sets itself, and achieves. Based on a written biography of the same name, the film does an excellent job of illustrating not only how much beyond even Cambridge-level professional mathematicians Ramanujan was, but also the absolutely fascinating way in which his mind worked. He repeatedly claimed that his insights were divinely inspired, often appearing to him fully-formed in dreams and visions of Hindu deities. His results were occasionally wrong, but were never less than astonishing in their originality and depth. They are still inspiring research today, close to a century after his death.

The film takes poetic license with a few aspects of Ramanujan’s life. His wife is depicted as an adult when in fact she was nine at the time of their marriage, for example. But these pale in comparison to the adroit handling of a story that needed to be told.

Highly recommended for anyone who likes mathematics or intellectual history.


The STEMpunk Project: Alternative Internal Combustion Engine Designs

After my post explaining how internal combustion engines work a number of friends were quick to point out that I hadn’t discussed some popular variants of the standard ICE design. To satisfy them and my own curiosity, here is a discussion of several less common adaptations of the internal combustion engine.

Note: to avoid excessive wordiness I will refer to the most common gasoline-powered internal combustion engine as an ICE, even though technically every engine below is an ICE.

Diesel Engine

Diesel engines and ICEs are pretty similar. The biggest difference is that, while an ICE draws the fuel-air mixture into a cylinder bore all at once, this process occurs in two stages in a diesel engine. Air is drawn into the cylinder bore during intake and fuel is injected near the end of compression. Diesel engines have no spark plugs; instead, ignition is achieved because diesels compress the fuel-air mixture more than an ICE, resulting in temperatures high enough to start combustion.

As you may have guessed this has consequences for the kind of fuel a diesel engine uses. Diesel differs from gasoline in that it is heavier, denser, and less flammable, but also has more energy per gallon. Diesels are often more fuel efficient than ICEs, but they are more expensive and can be harder to start, making them less optimal in colder climates.

Rotary Engine

A rotary engine follows the same four-part cycle of an ICE but is designed such that each part occurs simultaneously. The equivalent of a piston in a rotary engine is a rotor, which resembles a triangle with rounded corners and sides. It sits within a rotor housing that contains intake ports, exhaust ports, and spark plugs.

This housing is not cylindrical or spherical, but rather has a somewhat irregular shape like a circle with its north and south poles compressed slightly. The result is that a given rotor side is able to form larger and smaller spaces as it spins.  When the rotor passes over the intake valve it forms a larger space which draws in fuel-air mixture. It continues to spin and compresses the fuel-air mixture into a much smaller space, where a spark plug causes combustion. This drives the rotor and causes it to form another open space, with the exhaust generated by combustion being driven out of the exhaust port as that space closes.

When one side of the rotor is entering the compression stage, another side is finishing combustion and still another is beginning intake. There is also usually a second rotor in the same housing which is offset from the first by 180 degrees, meaning combustion is almost always happening.

Each rotor has a hole in the middle into which fits an eccentric shaft. The rotors are attached to the eccentric shaft at 180 degrees to each other, creating balance, stability, and low amounts of vibration. As in an ICE, the eccentric shaft is what transforms the rotor’s rotational motion into the vehicle’s propulsive force.

Compared to an ICE rotary engines have far fewer moving parts and generate a lot of power with relatively little size and weight. Their design does give rise to serious challenges with respect to preventing fuel and oil from leaking into places where it doesn’t belong. These challenges are met with an intricate series of seals both between a rotor and the housing and between rotors within the same housing.

Duke Engine

In an ICE pistons are attached at right angles to a crankshaft by connecting rods and arranged in a V or inline configuration. Igniting a compressed fuel-air mixture in the cylinder bore generates the power required to move the vehicle. An axial engine — of which the Duke Engine is but one modern incarnation — has its cylinders in a ring and attached to the crankshaft via a star-shaped component called a reciprocator. Each piston’s connecting rod is attached to one arm of the star, and the collective motion of all the pistons causes the reciprocator to spin. The reciprocator in turn is attached to the crankshaft in such a way that as it rotates the crankshaft spins in the opposite direction, with the result being that engine vibration is radically diminished.

Spark plugs and intake/exhaust ports are located on a stationary head ring positioned opposite the reciprocator. A spinning piston just starting its four-stroke cycle draws fuel-air mixture into its cylinder bore as it passes over an intake port, compresses it, passes over a spark plug which ignites the fuel-air mixture, expels the exhaust as it passes over an exhaust port, and then begins again.

This piston arrangement allows for the Duke Engine to be much smaller and lighter than an equally-powerful ICE, and with a greater fuel efficiency to boot. It also opens up myriad possibilities for experimenting with applications where the bulk and weight of a traditional engine have been problematic.


The STEMpunk Project: The Humble Washer

In As The World Opens I discussed the deeper appreciation I’ve gained for the infrastructure of civilization as a result of The STEMpunk Project. Today I want to reinforce that theme by satisfying a curiosity I’ve long held about a little piece of metal which is so ubiquitous that it’s nearly impossible to have done much tinkering without having encountered one.

I’m talking of course about washers, which you may recognize as these things:


washer is a small metal disc with a hole in its middle, like a doughnut. They are often found wherever a threaded fastener like a screw or a bolt is being used to bind multiple objects together. On many occasions, after having disassembled something I have dutifully put the washers back in place without having really understood their purpose.

People sometimes use the term “washer” to describe the gaskets used in plumbing to stop unwanted water leakage, but washers do a variety of things besides acting as seals. Perhaps the most important is that they work to evenly distribute force and load.

Imagine that you’re fastening two boards together with a screw. Getting a really tight fit means drilling the screw as far as possible into the board. As the screw head, still turning, comes into contact with the top board a tremendous amount of torque is generated. Many a novice carpenter has watched in dismay as a screw placed near the end of a board causes a nasty split in the wood, introducing a source of weakness. But placing a washer between the screw head and board greatly reduces the chances of such splitting because the torque is spread out over the larger, harder surface area of the metal disc.

Now imagine that you’ve used bolts to fasten a short board to a long board and have hung an equal weight from both ends of the long board. Where is all the resulting downward force concentrated? In the small area covered by the bolt as it exits the board! With a small amount of weight this isn’t going to be a problem, but it can become one as weight increase. The most common solution I have seen is to place a washer on the exit side and to use a nut to secure it in place. Here, the washer is both distributing the load of the weights and distributing the torque of the nut as its being tightened into place.

Why is it necessary to fasten things together so tightly that we risk splitting a board? In part because forces that aren’t of much consequence when making a bookshelf become extremely important when building a deck or chassis. As a vehicle runs it vibrates, and any bolts in the engine or body will begin to shake loose. As a deck weathers multiple seasons the wood of which it is made expands and contracts, compromising the integrity of the joints holding it together. If this shifting is extreme enough something important might break loose, causing injury or death.

With this in mind there are washer variants designed to keep even more tension on fasteners and joints. Star washers are built with teeth which bite into their point of contact, making them harder to dislodge. Belleville, wave, and curved washers all deform slightly when they are tightened down, increasing the pressure at the joint in a manner similar to how a compressed spring might.

This isn’t all that washers do. They can also be used as a kind of adapter whenever a bolt is too small for a hole, as spacers if a bolt happens to be too long, as boundaries between two metals like aluminum and steel whose contact will result in corrosion, and as electrical insulators.

So don’t make the beginner mistake of assuming that you can leave the washers off. They really are important!

The STEMpunk Project: Internal Combustion Engines.

I have begun the first stage of the mechanics module of The STEMpunk Project, my year-long attempt to learn as much about computers, electronics, mechanics, and robotics as I can. Naturally, this means I have been thinking about internal combustion engines, intriguing devices that can be found in a variety of machines ranging from lawnmowers to speed boats. All of them rely on the exothermic chemical process known as combustion, which occurs internally, hence their name.

The present essay is a broad-strokes discussion of the internal combustion engines found in modern motor vehicles, both because this knowledge will likely prove the most useful to me after my current project is finished and because I have to draw a line somewhere.

The majority of vehicles on the road are propelled by a four-stroke spark-ignition internal combustion engine. Vehicles on the less powerful end of the scale might only sport 3- or 4-cylinder engines while those at the other extreme contain 8- or even 16-cylinder engines.

There are a few different ways to arrange these cylinders within the engine block. In an inline configuration the cylinders are in a row, as the name suggests. Obviously there is a limit to how many cylinders can be made to fit in a straight line under the hood, so many engines have their cylinders in a “V” shape (hence the term “V-8”). One arm of the V will contain half the cylinders and the other arm will contain the other half, making better use of the space available. Less common than this are engines which have their cylinders laying sideways and the pistons moving left-to-right instead of up-and-down.

Each cylinder houses a piston, which is a metal drum that compresses the fuel-air mixture as it enters the cylinder cavity (also called the cylinder bore) and pushes exhaust out at the end of a full cycle. Each piston is connected to the crankshaft via a connecting rod, and it is the crankshaft which keeps all the pistons moving in sync. To prevent oil from leaking into the cylinder bore and exhaust from leaking out, each piston is wrapped in a set of rings which seals it in.

Internal combustion engines do not run on gasoline alone, but rather a mixture of air and gasoline together. In older vehicles and in simple, modern machines, the mixing of air and fuel is accomplished with a carburetor, but these days a fuel-injection system is more common. Air is brought into the engine and distributed to each cylinder by a series of tubes called an intake (or inlet) manifold. These come in numerous shapes, but a simple visualization of the manifold for a V-8 engine resembles a cylindrical octopus laying on top of the engine with one leg going to every cylinder.

Four-stroke engines are so called because each piston turns fuel into motion by going through four distinct strokes: intake, compression, power, and exhaust. During intake an intake valve at the top of the cylinder bore opens and the fuel-air mixture is drawn into the cylinder cavity by the downward motion of the piston. The piston then screams upward during compression, crushing the mixture into 1/8th or 1/10th its original volume, depending on the engine’s compression ratio. Then a spark plug ignites the mixture, beginning the “power” phase. The subsequent explosion drives the piston downward, with the resulting force being distributed to the tires and causing them to rotate.

Now the cylinder bore is filled with noxious fumes, and an exhaust valve opens at the top of the cylinder bore to allow the upward motion of the piston to expel them.

The spectacular synchronization between intake valves, exhaust valves, and pistons is achieved in part by a camshaft. The camshaft is a metal rod with tear-drop shaped lobes attached to it, each one of which connects through a rocker arm to either an intake valve or an exhaust valve. Rocker arms have a long side and a short side, and as the camshaft spins one lobe presses against the short side of a rocker arm which causes the long side to descend and open a valve.

These valves are spring loaded, so when the camshaft rotates and the lobe disengages its rocker arm the valve shuts again. Taken together the camshaft, valves, and rocker arms are called the valvetrain, and are connected to the crankshaft by a timing belt which keeps their motion in tune.

The result can be viewed as an exquisitely timed dance of fire and steel: a piston expels exhaust through an exhaust valve opened by a rocker arm, and is thus ready to begin its cycle anew; the crankshaft rotates, and the piston is drawn downward by its connecting rod; the camshaft rotates, synchronized to the crankshaft by a timing belt, and one of its lobes touches a rocker arm which opens the intake valve for the piston; the fuel-air mixture enters the cylinder bore, sucked in by the piston’s descent; the crankshaft continues to spin, now pushing the piston upward and compressing the mixture into a tiny space; there comes a spark, and an explosion, which fires the piston downward with great violence; the vehicle moves; the camshaft, bound by the timing belt to the crankshaft, now uses a different rocker arm to open the exhaust valve; the crankshaft sends the piston skyward again, and the exhaust is expelled.

This process naturally generates enormous amounts of friction. The engine is able to withstand this because much of its surface area is coated with oil, which in addition to lubrication also serves to marginally cool the engine down. The engine’s oil reservoir is called a sump, and usually sits below the crankshaft. An oil pump draws sends the oil to an oil filter before it is distributed by oil channels to the crankshaft bearings, cylinder bore, valvetrain, and anywhere else metal is touching metal. After performing it’s job the oil returns to the sump to be sent through the cycle again. Like everything oil breaks down eventually, which is why it must be regularly changed to keep the engine running smoothly.

But the cooling effects of oil are very minor compared to the tremendous amounts of heat created by combustion, which means that engines require an additional dedicated cooling system. While it is possible to air cool an engine, most vehicles rely on liquid cooling.

As the coolant of choice, water sits in a plastic tank waiting to be pumped throughout the engine. Because vehicles are expected to operate year round in a variety of different conditions the coolant must be protected from extreme cold by antifreeze and from extreme heat by being pressurized enough to push its boiling point up into a safe range.

A water pump sends the coolant through a number of hoses which spread like blood vessels through the engine, absorbing heat. When the coolant has absorbed as much heat as it is designed to, it is sent to the radiator. Consisting of many thin, usually horizontal tubes, the radiator is designed to “spread” the coolant out so that it releases the heat it has absorbed into the air, effectively carrying it away from the engine. Proper heat dissipation requires there to be a constant stream of air running over the radiator’s tubing; this is simple when the vehicle is going fast, but small electric fans are required to maintain airflow when the vehicle is going slow or at a stop.

Modern engines make use of ingenious devices to maintain the appropriate coolant pressure and temperature. The radiator pressure cap is built so that when pressure exceeds a certain threshold a small amount of coolant is let out into a reserve tank where it waits until it can be reintroduced into the cooling system. The mechanical thermostat is calibrated to open only when the coolant reaches a certain temperature. If the coolant is still cool it is recirculated through the engine, but if it has gotten hot it is sent to the radiator to cool down.

How then does the engine receive the initial spark it requires to turn over? Usually a lead-acid battery and an induction coil are used together to begin ignition, after which point the engine is somewhat self-sustaining. As the engine runs it spins an alternator, which is just a small generator inside the car that feeds energy back to the battery.

That covers the basics! Obviously there is a vast amount of additional material that could be included here. If time allows I’d like to write a bit about different engine types and engine improvements that could be on the horizon, as well as possibly getting a bit into the history of these remarkable contraptions that have done so much to shrink distances.

As always, thank you for reading.


The STEMpunk Project: As The World Opens.

She moved slowly along the length of the motor units, down a narrow passage between the engines and the wall. She felt the immodesty of an intruder, as if she had slipped inside a living creature, under its silver skin, and were watching its life beating in gray metal cylinders, in twisted coils, in sealed tubes, in the convulsive whirl of blades in wire cages. The enormous complexity of the shape above her was drained by invisible channels, and the violence raging within it was led to fragile needles on glass dials, to green and red beads winking on panels, to tall, thin cabinets stenciled “High Voltage.”

Why had she always felt that joyous sense of confidence when looking at machines?—she thought. In these giant shapes, two aspects pertaining to the inhuman were radiantly absent: the causeless and the purposeless. Every part of the motors was an embodied answer to “Why?” and “What for?”—like the steps of a life-course chosen by the sort of mind she worshipped. The motors were a moral code cast in steel.

They are alive, she thought, because they are the physical shape of the action of a living power—of the mind that had been able to grasp the whole of this complexity, to set its purpose, to give it form. For an instant, it seemed to her that the motors were transparent and she was seeing the net of their nervous system. It was a net of connections, more intricate, more crucial than all of their wires and circuits: the rational connections made by that human mind which had fashioned any one part of them for the first time.

They are alive, she thought, but their soul operates them by remote control. Their soul is in every man who has the capacity to equal this achievement. Should the soul vanish from the earth, the motors would stop, because that is the power which keeps them going—not the oil under the floor under her feet, the oil that would then become primeval ooze again—not the steel cylinders that would become stains of rust on the walls of the caves of shivering savages—the power of a living mind —the power of thought and choice and purpose.

Atlast Shrugged, Ayn Rand

In the classic film American Beauty there is a famous scene wherein one character shows another a video of a plastic bag as it’s blown about by the wind. In whispers he describes how beautiful he found the experience of watching it as it danced, and amidst platitudes about “a benevolent force” he notes that this was the day he fully learned that there is a hidden universe behind the objects which most people take for granted.

One of the chief benefits of The STEMpunk Project has been that it has reinforced this experience in me. While I have thoroughly enjoyed gaining practical knowledge of gears, circuits, and CPUs, perhaps the greater joy has come from a heightened awareness of the fact that the world is shot through with veins of ingenuity and depth.

Understanding the genesis of this awareness requires a brief detour into psychology. Many people seem to labor under the impression that perception happens in the sense organs. Light or sound from an object hits someone and that person observes the object. Cognitive science shows definitively that this is not the case. Perception happens in the brain, and sensory data are filtered heavily through the stock of concepts and experiences within the observer. This is why an experienced mechanic can listen to a malfunctioning engine and hear subtle clues which point to one possible underlying cause or another where I only hear a vague rattling noise.

As my conceptual toolkit increases, therefore, I can expect to perceive things that were invisible to me before I had such knowledge. And this has indeed been the case. More than once I have found myself passing some crystallized artifact of thought — like a retaining wall, or an electrical substation — and wondering how it was built. That this question occurs to me at all is one manifestation of a new perspective on the infrastructure of modern life which is by turns fascinating, humbling, and very rewarding.

I have begun to see and appreciate the symmetry of guard rails on a staircase, the system of multicolored pipes carrying electricity and water through a building, the lattice of girders and beams holding up a bridge; each one the mark of a conscious intelligence, each one a frozen set of answers to a long string of “whys” and “hows”.

This notion can be pushed further: someone has to make not just the beams, but also the machinery that helps to make the beams, and the machinery which mines the materials to make the beams, and the machinery which makes the trucks which carries raw materials and finished products to where they are needed, like ripples in a fabric of civilization pulsing across the world [1].

It’s gorgeous.

A corollary to the preceding is an increased confidence in my own ability to understand how things work, and with it a more robust sense of independent agency. For most of my life I have been a very philosophical person: I like symbols and abstractions, math, music, and poetry. But if every nut and bolt in my house was placed there in accordance with the plans of a human mind, then as the possessor of a (reasonably high-functioning) human mind I ought to be able to puzzle out the basic idea.

Don’t misunderstand me: I know very well that poking around in a breaker box without all the appropriate precautions in place could get me killed. I still approach actual physical systems carefully. But I like to sit in an unfinished basement and trace the path from electrical outlet to conduit to box to subpanel to main panel. On occasion I even roll up my sleeves and actually fix things, albeit after doing a lot of research first.

In fact, you can do a similar exercise right now, wherever you are, to experience some of what I’ve been describing without going through the effort of The STEMpunk Project. Chances are if you’re reading this you’re in a room, probably one built with modern techniques by a contractor’s crew.

Set a timer on your phone for five minutes, and simply look around you. Perhaps your computer is sitting on a table or a desk. What kind of wood is the desk made out of? Were the legs and top machine-made or crafted by hand? If it has a rolling top, imagine how difficult it must have been for the person who made the first prototype.

Does the room have carpet or hardwood floors? Have you ever seen the various materials that go under carpets? Could you lay carpet, if you needed to replace a section? Are different materials used beneath carpet and beneath hardwood? If so, why?

You’re probably surrounded by four walls. Look at where they meet the floor. Is there trim at the seam? What purpose does it serve, and how was it installed so tightly? Most people know that behind their walls there are evenly-spaced boards called “studs”. Who figured out the optimum amount of space between studs? How do you locate studs when you want to hang a picture or a poster on your wall? Probably with a stud finder. How did they find studs before the stud finder was invented?

Does the ceiling above you lay flat or rise up to a point? If it’s a point, have you ever wondered how builders get the point of the ceiling directly over the center of the room? Sure, they probably took measurements of the length and width of the room and did some simple division to figure out where the middle lies. But actually cutting boards and rafters and arranging them so that they climb to an apex directly over the room’s midpoint is much harder than it sounds.

If you do this enough you’ll hopefully find that the mundane and quotidian are surprisingly beautiful in their own way. Well-built things, even just dishwashers and ceiling fans, possess an order and exactness to rival that of the greatest symphonies.

I’m glad I learned to see it.


[1] See Leonard Read’s classic essay I, Pencil, for more.

It’s Not Always About the Message.

There are plenty of books out there whose value derives from the fact that they challenge previously unshakeable assumptions and thus raise profound new questions. A good example is Julian Jaynes’s The Origins of Consciousness in the Breakdown of the Bicameral Mind. In it he draws on linguistic analysis, exegesis, art, and myriad other disciplines to argue that peoples such as the ancient Greeks simply weren’t conscious in the same way modern humans are. The result is difficult to dismiss, despite how crazy it might sound upfront.

There are also plenty of books out there whose value derives from the fact that they expand areas of knowledge which you hadn’t even realized you were glossing over. I didn’t realize how little I knew about Pre-Columbian American Indians before I read Charles C. Mann’s 1491. Though I had cursory knowledge of the Incas, the Toltecs, the Mayans, the Iroquois, and so on, reading an extended treatment of their respective societies opened my eyes to a richness and diversity I hadn’t been aware of.

But there are many valuable books which don’t do anything more than tell you something you already mostly knew, but in a way that makes the knowledge more resonant and actionable. Two of my favorite books are Josh Waitzkin’s remarkable The Art of Learning and Cal Newport’s outstanding Deep WorkThe thesis of the former is “you should spend a lot of time mastering the fundamentals of a field” and that of the latter is “you need to focus intensely with very few distractions to make progress on high-value problems”.

I doubt anyone reading this with find these two insights revelatory. And yet I have re-read The Art of Learning maybe a dozen times. It isn’t the message per se that I love, but the author’s pellucid and accessible style together with illustrations from his life as a star in competitive chess and martial arts. Seeing the astonishing results obtained by a person who so totally embodies his own simple philosophy inspires me to try to do the same. Similarly, when I read Cal Newport’s books and essays I don’t get the sense that I’m in the presence of a mind substantially better than my own. Instead, his success seems to come from the ruthless application of a handful of basic techniques, all of which I understand (but don’t practice) just as well as he does.

So if I were to write a book that boils down to “exercise is good and you should be doing it”, it might not seem like it would be worth reading. But if I were to couch this bromide in stories about how a grandmother used exercise to reclaim the ability to play with her grandchildren, or built a philosophical justification for exercise by relating it to various historical warrior traditions, many people who already endorse the basic message might be compelled to act on it more consistently.

This is worth bearing in mind from the perspective of both a potential writer of and reader of books. It’s not always about the message.

The STEMpunk Project: Fifth Month’s Progress

Because July was mostly spent reading and watching youtube lectures I’ve opted not to include a picture this month.

During the computing module I was able to maintain fairly sharp boundaries between the three different stages, but this was much less so in the electronics module. Trying to make sense of even basic circuits required me to spend at least a little time digging into theoretical discussions of voltage, current, power, and resistance, and while I did talk an electrician into letting me work for him, it looks like that’s not going to happen for a few weeks, so I’ll have to wait until then.

Nevertheless, I read most of “Basic Electricity”, a dense little manual written by the U.S. Navy, which I complemented with Dave Grynuik’s informative and entertaining course on beginning electronics. I also watched a number of videos on residential wiring, with a special emphasis on wiring breaker boxes and electrical subpanels (see 1, 2, 3, 4).

Further, I managed to write posts on batteries, transistors, the differences between three common means of storing charge in a circuit, and a basic treatment of the theoretical foundations of electronics (linked above). Though not directly STEMpunk-related, I also explored the existence of a fascinating quiet spot in the electromagnetic spectrum and reviewed James Michener’s excellent novel “Space“.

Not a bad haul!