The Two-Egg Problem...

Examined in detail in a most geekly fashion.  Great geekly stuff!

What Does This Mean?

I've been watching the T-bond rate for months now, as it decends to impossibly low interest rates.  From highs of over 15% APR in the early '80s, it has dropped to just over 1.5% APR as of Friday.

This is an absolutely incredibly low interest rate.  These interest rates are set by auction; by definition this means that there are plenty of borrowers (the buyers of the bonds) willing to lend the U.S. billions of dollars at these absurdly low rates.  If 1.5% doesn't really mean that much to me, here's another way to look at it: would you lend the U.S. government $1,000 for ten years, in exchange for $15 a year?  That's exactly what thousands of willing lenders, lending an aggregate of many tens of billions of dollars, are doing.

What on earth is wrong with these people?  Why would they do such a thing?  It especially seems to fly in the face of reason when you see the size (and rate of increase) of the U.S. debt, nicely shown on the graph at right.  In this sort of situation, one might reasonably expect to see inflation – which would make you very reluctant indeed to lend money at such low rates.

I've read dozens of articles claiming to explain this phenomenon.  They all boil down to some combination of two things:

– U.S. Treasury Bonds are the least bad place to park your money right now (in other words, the most likely place to give you your money back).  Because of that, it's a seller's market – lenders trip over each other competing for the chance to buy T-bonds.  The problem I have with this explanation is that 1.5% APR is hardly any better than stuffing money in my mattress.  I don't find this argument particularly persuasive.

– the smart lenders are persuaded there is almost no risk of inflation in the U.S., because of the success of the Fed in managing it.  This is so implausible that I simply cannot believe even the stupid money would believe it, much less the smart money.

So I am left completely puzzled by this phenomenon.  Any of my readers have any ideas?

Puzzler...

All but one of you got the correct answer to last week's puzzler: the reason why one lighting technology is more pleasing to the eye than another is the smoothness of the intensity of light it emits over the visible spectrum. Incandescent bulbs have a very smooth spectrum curve, with the very best of them (high-temperature halogen) emitting a spectrum that closely resembles that of the sun.

The two technologies that offer the best hope for energy saving (compact fluorescent and white LED) have emission spectrums that are very “peaky”. For example, a white LED typically emits 90% or more of its light in either two or three very narrow bandwidths. If an object that is illuminated by such a lamp happens to be colored such that it doesn't match the colors emitted by the lamp, then it will appear to be a different color than it would have in sunlight (or incandescent light). If you've ever seen the peculiar way things look under low-pressure sodium street lamps (the yellow ones), then you've seen an extreme example of this. CFLs and LEDs aren't quite that bad, but to anyone who appreciates colors they can be very annoying. Perhaps even worse is a different phenomenon, often called “harshness”. This has to do with the opposite situation: when an object illuminated by CFL or LED light happens to be a color that matches the peak emission. Such an object has a peculiarly high intensity, almost as though it were glowing on its own. In reality, the object is reflecting more light than it would under sunlight of the same average brightness – another effect of the “peaky” emission spectrum – and our perceptual system interprets this as that almost-self-glowing effect.

Manufacturers of CFLs and LEDs are working to improve this discontinuous spectrum problem. In the case of CFLs, that means better phosphors and compromises on efficiency. There are multiple technologies being used and developed for LEDs, and I think in the long term the best LEDs are likely to be superior to the best CFLs (this is not true today, however).

This week's puzzler is back to history. As usual, no fair googling before you answer!

America has had a series of violent episodes in its schools, and many Americans believe the incidents are escalating both in severity and in frequency. That's actually a challenging thing to determine, as our population has increased rapidly throughout our history, and the number of schools (and the number of children in those schools) has varied greatly. This complicates analysis and comparison. But at least one data point is very easy: the worst incident of school violence in American history left 38 students dead. What year did this incident occur in?

Puzzler...

Last week's puzzler had more wrong answers than I usually see – chaparral esoterica must not be the repertoire of most of my readers! But, having said that, I must also say that more than half (about 57%) of you got it right: chaparral plants are generally of uniform size because they're all about the same age. They're all the same age because many of the chaparral plants require fire for their seeds to germinate – so they all sprouted in the year or two following the last fire that burned over the area. In the case of Lawson Valley, where I live, that last happened in 1973.

This week's puzzler is on a technology phenomena. There are only a few choices of technology that can light your home in the absence of sunlight: flames (candles, gas lights), materials heated to incandescence (incandescent bulbs, halogen lamps), fluorescence (fluorescent lamps, CFLs), photonic emission from plasma (neon lamps), and light-emitting semiconductors (LED lamps). All of these technologies produce light, but the light produced is not all the same.

This is something anyone can readily observe, without any instruments: observe any ordinary, multi-colored object under the various kinds of lighting and they look different under each kind, even if the brightnesses are the same. Women know that their makeup looks different under incandescent lighting than it does under fluorescent lighting. Similarly, photographers and painters are picky about their lighting sources, because their subjects will look different under different kinds of lights.

When people can freely choose the type of lighting they want, without being constrained by cost or considerations of efficiency, they will almost always choose high-brightness incandescent lighting (such as halogen lamps). Several studies have tested thousands of subjects in side-by-side tests. The study that most impressed me put people in a room where light was “piped in” in such a way that they could not determine its source. The test subjects were given a switch and a dimmer control that let them choose between incadescent bulbs, halogen bulbs, CFLs, traditional fluorescent lamps, and LED lamps (though the test subjects didn't know which kind of lighting corresponded to which position of the switch). They were asked to choose the kind of lighting and the lighting level that they though was most pleasing. The room contained furniture, pictures on the wall, and a table full of magazines. Over 98% of the test subjects chose halogen lighting at within 10% of maximum brightness.

Here's the question: what exactly is it that makes one lighting technology more pleasing to the eye than another?

Puzzler...

Well, not very many people attempted to answer last week's puzzler – but everyone who did got it right. What is the middle name of a former U.S. Senator who started his career as a gambling judge, and ended it as a shamed, alcoholic Senator? The answer is Raymond, as in Senator Joseph Raymond McCarthy.

This week's puzzler is back to science. In the chaparral where I live, it's very common – normal, in fact – to find large areas where most of the commonest plants (manzanita, ceonothus, etc.) have a very narrow distribution of size. For instance, where I live nearly all of the manzanita specimens are between 4 and 8 feet high. In most other plant communities, you'll find a much broader distribution of sizes. Why are chaparral plants so uniform in size?

Puzzler....

Well, nobody got the right answer to last week's puzzler: how did the vacuum tube manufacturers get the high quality vacuum in such an inexpensive, mass-produced item? The correct answer is the inductively heated barium reactor, known colloquially as a “getter”. These were very simple and cheap: just a piece of sheet metal coated with a barium compound. The barium, when heated, absorbed any gas remaining inside the tube. Typically the manufacturers heated this little piece of sheet metal inductively (meaning by placing the tube in a powerful, rapidly changing magnetic field). This caused currents (“eddy currents” to flow in the sheet metal, and that caused it to get very hot. So hot, in fact, that the barium coating would flash-vaporize (absorbing gas as it did so). This vapor would then cool and adhere to the inside of the glass envelope of the vacuum tube, causing the silvery coating familiar to anyone who has handled vacuum tubes.

This week's puzzler is back to history – in this case, 20th century U.S. history. What was the middle name of a former U.S. Senator who was a judge early in his career (and was a notorious gambler while on the bench), enlisted in the Marines in 1942 to fight (despite his exclusion from obligatory service because he was a judge), came back from the war and successfully ran for the U.S. Senate (despite well-documented lies and self-serving distortions about his military service record), became a highly polarizing figure in the Senate and finally died in office, a bitter and often inebriated man? The clincher is that modern historians are starting to look at his Senate record a little more positively; in fact, some have posited him as one of the early victims of wrongful media demonization.

Puzzler...

Most of you got the right answer to last week's puzzler: the orange and yellow flames in a wood fire are caused by particles (mainly carbon) heated to incandescance. The physics of burning wood is far more complex than you might think at first glance. The actual combustion that takes place happens between gases, including ordinarily solid materials that are heated to the point where they change state into a gas. If you see blue flames, that's actually a direct result of combustion – but much of the combustion takes place without emitting any light at all in the visible spectrum. Where things get really complicated is the conversion of the cold, solid wood into superheated gases ready to combust. The simplistic picture is a combination of radiant head and convective heat (from the gas combustion) heats the wood to the point where it decomposes to simpler compounds or elements, in gaseous form. The details are far more complex, and still not completely understood...

This week's puzzler is technological:

Up until the late 1960s, most electronic devices employed vacuum tube amplifiers as their fundamental component. These vacuum tubes were one of the first “high-tech” devices manufactured in very high volumes. There were several challenges in their manufacture, but one of the big ones was how to produce the extremely high-quality vacuum inside the tubes. How did they actually accomplish this?

As usual, no fair googling until after you've answered...

Puzzler...

Less than half of you got last the correct answer to week's puzzler (and I got one complaint about the obscurity of the question!).

Trofim Lysenko was a biologist working in the Soviet Union from about 1925 through the 1960s (he died in 1976). He promoted the notion of inheritence of acquired characteristics – an idea that was popular prior to the early 1900s, when science started to understand genetics. A simple example of inheritance of acquired characteristics: if you wanted pigs without tails, you'd cut off the tails of a male and female pig, breed them, and their descendants would have shorter tails. Lysenko (and other proponents of the inheritance of acquired characteristics) were not at all put off by the total failure of experiments to produce such results – they had an endless stream of explanations and flawed experiments “proving” the theory.

But Lysenko's main skills weren't scientific at all: they were political. By 1948 he managed to promote his ideas so effectively within Stalin's Soviet Union that he persuaded Stalin to legislate the “correctness” of his theories – outlawing Mendeleevian inheritance (modern genetics) in the process. Thousands of biologists were imprisoned or sent to gulags; hundreds died. Soviet biology, as a direct consequence, was set back decades, and was the laughingstock of the west. Not until 1964 – long after Stalin's death – was the official mandate for Lysenkoism removed, and not until then were Soviet biologist free to pursue modern genetics. It was a disastrous example of politicized science. Think about that, and then consider what has happened over the past few years with respect to the science of global warming. Political suppression of scientific debate is dangerous, and we have a frightening example of why in our recent history…

This week's puzzler is a science question: when wood is burning in a fireplace, you can see yellow or orange flames, sometimes blue flames, and red or orange embers. What is actually causing those yellow or orange flames?

Puzzler...

Well, 11 of 14 people got last week's puzzler right – you can build an entire computer using nothing more than two-input NAND gates (and actually, you can build one from two-input NOR gates as well). The fact that so many of my readers knew this answer certifies my audience as being mostly comprised of fairly extreme geeks...

This week's puzzler is back to history – science history...

What was the last name of the scientist who (in the early 1900s) was notoriously associated with the notion that acquired characteristics of an organism could be inherited? This scientist's views persuaded the leader of a major country, and caused Darwinian inheritance to be officially banned there for many years.

No fair googling!

Puzzler...

Last week's puzzler asked this: at about what altitude is the air pressure half that of sea level? The answer is 18,000 feet, which almost half of the respondents got right (5 of 12), as you can see at right.

Something you may not know is that the air pressure declines exponentially as the altitude increases. For about every 18,000 feet of altitude gain, the air pressure halves – so at 36,000 feet the air pressure is about 1/4 that at sea level, at 54,000 feet it's about 1/8 of sea level, and so on.

This week's puzzler is about the early history of a technology that is ubiquitous today: the digital computer. It is entirely possible to build a digital computer from a single logic component. Before integrated circuits made all sorts of logic components cheap and easy, there were some advantages (especially for maintenance) in having a computer built from such a simple set of components. One of the small computers I worked on in the Navy was made this way. What is one of the logic components from which you can build an entire computer?

Puzzler...

Last week's puzzler was this: what caused the “erratic boulders” that are found all over the country of Estonia? Most of you (13 of 17) got it right: the erratic boulders were left by the retreating glaciers. The boulders were originally scraped from the pink granite bedrock exposed in northern and southern Finland, and then carried hundreds of miles south to Estonia. As the glaciers melted, the boulders gradually descended until finally they were left on the bare limestone ground of Estonia. The Vikings carved runes into some of these boulders, and examples of such carved boulders can be seen in many locations in Estonia. In addition, the local cultures paid attention to many of them (especially the larger ones), and many of the boulders have footpaths to them, and ladders to climb them, and these are maintained to this day. A popular roadmap made by an Estonia company has the location of hundreds of these boulders marked, and in my travels around Estonia I have visited dozens of them, just for fun.

This week's puzzler tests your knowledge about the Earth's atmosphere. You most likely know that the atmospheric pressure is highest at sea level (well, actually, at those points on the Earth that are below sea level), and that the pressure falls as you go to higher and higher elevations. But at what altitude does the atmospheric pressure fall to half the pressure at sea level?

No fair Googling until after you answer!

Puzzler

The correct answer to last week's puzzler was “Gunter's Rule”. You can see one from my collection here.

For this week's question, we turn to natural history. Nearly the entire country of Estonia has a similar geological makeup: a thick layer of limestone covered by a thin layer of soil (which is chock full of limestone rocks). However, almost anywhere in Estonia you can find rocks (some as large as a house) made of a pinkish granite. These rocks are called “erratic boulders” by geologists, and they are more common in Estonia than anywhere else in the world. How did the erratic boulders get there?

As always, no fair googling…

Puzzler...

Well, the last puzzler apparently wasn't all that puzzling: everybody who answered was at least close. If you're interested in the story of the cargo ship SS Mayaguez, you can read about it here.

Meanwhile, here's a new puzzler:

As long ago as the late 1600s, Europeans were using a straight piece of material (usually wood, sometimes ivory or brass) much like a ruler with special markings to make all sorts of calculations, including multiplication, division, trigonometry, and logarithms. This device was normally used in conjunction with a pair of dividers (a compass with two metal points). It was as ubiquitous amongst the engineers and scientists of the day as computers and calculators are today – but today it is virtually unknown and unheard of. What was this device called?

Puzzler...

Last week's puzzler:

It seems like forever since I posted the last puzzler, about a strange early form of main memory for digital computers.

The correct answer was “mercury”, which got 41% of the 98 votes on this puzzler. To the best of my knowledge, none of the other elements figured in any early computer memory system, though silicon of course is the main constituent of current memory systems.

As one commenter noted, mercury was used in an early memory system that was essentially an acoustic delay line. The system that I worked on used long glass tubes of mercury, bent into a spiral much like a fully compressed spring. Each tube was about three-quarters of an inch in diameter, bent into a spiral that was about six inches in diameter and about four feet long. That means that the tubes, if fully extended, would have been about 100 feet long. The glass was coated with a soft plastic coating that was intended, I think, to provide some high-frequency acoustic isolation. The system had something like 40 of these tubes, providing a 30 bit word with error correction (the extra 10 or so bits). I can't remember some of the interesting details, such as the acoustic frequency or the number of bits held in each delay line. I do remember the main maintenance issue: thermal control. The operation of the system depended on (for those days) very tightly controlled, steady and even, temperatures across the entire array of tubes – not an easy thing to do.

This week's puzzler:

For this week's puzzler, I'm going back to history – this time, a little piece of American history that I happened to witness while I was serving in the U.S. Navy. As always, no fair Googling until you answer!

Puzzler...

An eon or so ago, I posted a puzzler that asked what business Samuel Clemens (Mark Twain) got into that bankrupted him. Half the people responding (that would be two people) got the right answer: a typesetting machine. More specifically, his investments in the Paige Compositor (more here) did him in financially.

This week's puzzler delves into the history of digital computing, specifically into the history of a computer's “main memory” (today known as RAM, for Randomly Accessible Memory). In the early days of digital computers, main memory was one of the biggest engineering challenges. There were no integrated circuits at all, much less the massive RAM chips we have today. Magnetic core memory was the mainstay of main memory for a couple of decades – but before core memory, there were other technologies used. For example, magnetic drum memory was used into the mid-1960s on some computers. Some of these earlier technologies seem quite exotic and bizarre by today's standards, far more complicated and less capable than seem normal today.

One of these technologies was still in use (albeit not commonly) in the U.S. Navy when I went through computer technician school in the early 1970s. Even then it seemed like a museum refugee! But I was trained to repair and maintain this main memory, though thankfully I never saw one once I left school. Today's puzzler is this: what chemical element did a once-popular main memory technology depend on?

Weekly Puzzler

Last week's puzzler got some interesting results: exactly half the people who answered got the right answer (picking a random number), and the other half all picked the same wrong answer (computing the angular distances between all the stars in the sky).

Despite experiences you may have had with a computer that seem like random events, computers are actually deterministic devices – for a given set of inputs, they always produce the same results. Computers have no capability that is the equivalent of rolling a pair of dice; they simply don't know how to. Some very clever programmers have developed some very clever approximations to random number generation, but even the cleverest of them is still repeatable: given the same set of starting conditions, they generate the same darned numbers, every time.

It is possible to build special-purpose computer hardware to generate truly random numbers. Such hardware usually depends on some natural phenomenon (such as radioactive decay) that is, so far as anyone knows, truly random. Some innovative folks in recent years have developed other, less expensive techniques. For example, one such technique involves a lava lamp and a digital camera watching it; the image is then compressed to generate random numbers. To my knowledge, nobody has yet proved whether these systems are truly random…

This weeks puzzler is another history factoid...

Puzzler Update

Only two people even guessed at the name of the first microcomputer kit, and both got it wrong. The kit was called the "Jolt", and it was a very simple 8008-based design with just a numeric keypad and two seven-segment LED displays as I/O.

This week, back to science and technology.

Imagine that you had access to an infinitely powerful, infinitely fast digital computer. Which of the listed tasks would be impossible for even this computer to perform?

This Week's Puzzler

This week we delve a little into the history of technology – relatively recent history, which I am ancient enough to have personally participated in!

The ubiquitous personal computer is based on a “microcomputer chip” such as an Intel Pentium. Microcomputers first appeared in the 1970s, initially as the brains behind primitive four-function electronic calculators. Several companies produced early microcomputers powerful enough to be considered a general purpose computer, but arguably the first such microcomputer was the Intel 8008 – a primitive and slow little computer that was nevertheless quite a revolutionary device.

Unlike most earlier digital computer technology, the 8008 was cheap enough to be accessible to the hobbyist community, and a tiny little company produced an 8008 kit within weeks of the chip's initial release. This kit created quite a stir in the hobbyist community, and hundreds of nutcases like myself bought one. The kit was really just a bag of parts and a schematic – to assemble the kit required mainly wire-wrapping, a bit of soldering, and the ability to provide an adequate power supply.

I had my kit assembled and running in two days, and I was thrilled – I actually personally owned a computer! At the time, I was a DS (computer repair technician) in the U.S. Navy, and the computers I worked with there were the size of a large refrigerator – and yet not as powerful as the little 8008 that I kept in a cardboard box. I'm sad to say that I've long since lost that assembled kit. Advances in technology were fast even then, and it was only a year or two until that kit was obsoleted by a succession of more advanced microcomputer systems, based on chips like the 8080, Z80, 6800, and 6502.

What was the name of that wire-wrap 8008 kit? Display your geekiosity, and vote your answer at right...

This Week's Puzzler

Update and bump:

Simon M. writes with a question about exactly what “thread count” actually means. There are two ways one could interpret that phrase: that in one square inch there are 200 threads (counting the threads going in both directions, so 100 in each direction), or that there are 200 threads per inch going one way (so 400 going both ways). I'm not sure what the correct use of that terminology is, but … for the purposes of my puzzler, I mean the second definition (200 going each way in a square inch, for 400 threads all together).

Original post:

Suppose you have a bed sheet that is exactly 6 feet wide and 8 feet long, with 200 thread count. If all the threads that comprise the sheet were laid end-to-end, how long would the resulting thread be (in miles)?

Cast your vote at right…

Last Week's Puzzler

To be fair, there is some legitimate debate about which tyrant was the worst of the lot. Specifically, there are some reputable historians who believe Josef Stalin was the worst of the lot, and others who believe (mainly on the basis of recently revealed evidence) that Mao Tse Tung was the one. On the basis of what I have personally read, I'd say the preponderance of the evidence would give Mao the nod.

George W. Bush (I knew someone would vote for him!) doesn't even place in the top 100 on this scale.

I expected many more people to vote for Adolf Hitler, based on his notoriety – my readers are apparently better informed than most Americans…