Donald Trump is the billionaire leader of Christians in the United States today. We might as well face facts. Some are saying that Trump has been a Christian for years. Leaders of southern fundamentalists inside the United States, like Franklin Graham,  joined forces with Russia and Israel to make him president.

It’s true.

Prophet Cindy Jacobs told attendees at Revolution 2017an event held at the Museum of the Bible in Washington DC  (God’s base camp, she called it) — that President Trump ”will be seated and mantled with the power of God.”

I’ve written several essays on the takeover of America by southern evangelicals, like Jerry Falwell Jr., who made a deal with the president to advance his vision of an America submitted to GOD’S WILL, as he himself discerns it.  Links to these articles are provided at the end of the essay for those who might want to review them.

I’m writing this essay, because it seems like the entire country is in denial about what is going on. People driven crazy by religion have embedded themselves into the politics of USA! USA!  and are working overtime to transform the country into their own twisted vision of what they think God wants.

While rabid wolves circle disguised as sheep, the rest of America is starting to understand that it is being enveloped and smothered by a Jim Jones style cult, which some fear will get us killed, because these hypocrites (and they are hypocrites) plan to force their despised and unloved flocks to swallow a strychnine-laced Kool-Aid of evil that will poison the earth with the trauma of mass-suicide and murder.

These sycophants of power want to hasten the “end-times” as foretold in the book of Revelation, which comes last in the Bible; it is an incomprehensible tract that is the capstone of their “eschatology.”

They hope to mess-up the world so thoroughly that it will force a “rapture” that will sweep them up into Heaven as their enemies are tortured and killed.

In their wicked minds, pedophilic converts and sexually abusive power-trippers make the book of Revelation a mirror for the worms that crawl through the chambers of their raging hearts.

If you aren’t scared, you should be.

Their inspiration comes from the book with the passage they don’t memorize or quote, because they are blind guides. They just kind of skip over it as they flit their way to paradise and leave the rest of us behind.

Your merchants were the world’s important people. By your magic spell all the nations were led astray.  Revelation 18: 23b (NIV)

They seek the power and glory of wealth that is too often hidden in the folds of a prayer shawl.

…the deceitfulness of wealth chokes the word, making it unfruitful.  Matthew 13: 22b (NIV)

Billy Lee

Note from the Editorial Board:  Every member of the Editorial Board advised Billy Lee not to publish his latest tome, because it might be misunderstood, which would be bad; or it might actually be understood, which would be worse.

In defense of Billy Lee, during its first year the single victory in law of the current national leadership was to lower its own taxes, which were already too low by half.

It was reminiscent of one of the parables: the rich young ruler.  Obviously, our leaders read the parable and modeled their behavior after this eager-to-please young man of the Bible. For those not familiar, click on the link.

In fairness, we would be remiss not to mention that the president continues to repeal everything ”Obama.” So, it isn’t all bad inside the USA — at least for those Americans who hate Kenyan-born, Muslim presidents who misplace their birth certificates.

Our current president led the crusade to expose the ”truth” about President Obama, and many Americans believed it. Think of the good causes our Christian president put together to expose how vile and evil was our first Negro president. He exposed crooked Hillary too, and lying Ted, and little Rubio, and sloppy Steve, and — as we just said — that other low-life he hates, nigger Barry.

No wonder southern evangelicals and the GOP love him. He is our leader — our president — and we must all, every one of us,  learn to love him too, right? — we must abase ourselves before him — because he is a stable genius, if for no other reason. 

The Billy Lee Pontificator Editorial Board

Hating Christmas

Beverly Mae and me live on a cul-de-sac with a lot of old people everywhere. Some of the houses are empty; folks go to Florida, mostly. Some travel to second, third, or fourth  homes located only God knows where. None have Christmas decorations. It’s too much work when people are old and no one comes to visit.

A black kid who must have spent a lot of time making Christmas candles came to our house yesterday. He displayed his wares and gave what I thought was a carefully memorized pitch for the homeless.

How much? I asked.

Most folks give twenty dollars, he said.  I held an IPhone at the ready pre-dialed to  911 in case he tried to rob me.

After looking the boy over, he seemed like a good kid, so I put the phone away and paid the money. The last thing he said as he stepped back to leave was, Thank you, sir, for answering the door. It means a lot at Christmas.

I wondered if I should tell him that the reason people weren’t answering their doors was that they had already left town, most of them.  No, I thought. Better not tell him that.

People live in my neighborhood who, I think, must be more paranoid and racist than me. Some no doubt refused to answer, because they darn well aren’t going to deal with a door-to-door salesman at Christmas-time.  Especially if they look like someone who might hate them for being unable to feign even a little trust — a little kindness and love —  during the Christmas season. It’s scary when strangers approach the house who are male, black, and have never been seen before.

Christmas is supposed to be white as snow, right?

What if I misjudged the young man? Is it wise to tell someone just because they present well that the neighborhood is empty? Their friends might come back to pillage and loot.

Cul-de-sac where Billy Lee lives.

Yeah, it’s going to be a crummy Christmas.

Here are ten things I worry about that make this end of year holiday season especially depressing  — and it’s not the weather, which right now is grey and overcast.

  1. The GOP raised taxes on 25% of the public. Guess who made it into that illustrious group? Me.  I’m in — according to a questionnaire about finances conducted by the New York Times.
  2. The president left the White House without wishing the country a Merry Christmas!  It’s another campaign promise the oinking chief-commander broke.  What good is being free to say Christmas if the president won’t say it? Everyone should be used to his lying-ways by now. Sorry — the fat-man continues to irritate me.
  3. Will the president start World War Three on Christmas Eve? It’s just one more thing to worry about. I’m not going to bed with visions of sugar plums dancing in my head this time. Will he obliterate North Korea because they tested bombs and missiles, something the USA has done thousands of times? Who the hell knows?
  4. Will he fire Robert Mueller, a decorated Marine veteran and arguably one of the most honest men in government? Or will he perhaps fire a random person on Christmas, because, why the hell not?  It’s Christmas, people! The orange-man demands results. He doesn’t mess around when it comes to making America great. He fired the former FBI director, James Comey, because his attempt to clear Hillary Clinton three days before the election failed. You’re fired! quacked the presidential duck. He did it for Hillary. He really did. He was helping an old friend. That’s all it was. I watched him say so on television. Maybe it was fake news. I can’t tell anymore.
  5. One of the best gifts? Trump gave Americans the precious gift of the ObamaCare Repeal. It’s what he said. I saw the video on the nightly news. He promised to replace it with something way better.  Can’t wait to open that present. Unaffordable healthcare is a wonderful thing. It prevents countless thousands of Americans from going to hospitals where they risk being hurt by doctors who are only in it for the money.
  6. Family members who have shopped say the crowds in the stores are minimal. Despite the commercial hype on billionaire-owned media, store sales have crashed.
  7. The stock market noticed. It’s down. Yes, Russian oligarchs  are playing games by pulling out money. It’s a fun prank, especially during Christmas. Why not? I confess; I cut back on Christmas spending. The economy can go belly-up — I really don’t care. I don’t put money in the stock market; I don’t vacation in Vegas. The wealthy are on a shoplifting-spree, like under former President Bush. The greed of his fellow-travelers crashed the country in 2008. The current fool’s friends are worse. So will be the results. How long will profiteering take to cut the legs off the middle-class this time around? Not long, methinks.
  8. Churches campaigned for the biggest boob ever to run for the highest office ever in the history of the world ever and of all  human-kind, ever. He’s huge, the orange fat-man. Churches organized bus-runs to take congregants to hear Franklin Graham  “on tour” who pretended to anyone who listened that he was politically neutral while he ranted against witches (like the unnamed evil Methodist, Hillary) and abortion.
    Omarosé Onée Manigault-Newman predicted that people would bow before our new leader before history as we know it ends. Omarosa is one of the many misfit toys the orange man fired during his climb to ultimate power.
    How can anyone go back to those crazy churches should their bozo-president actually screw-up everything at Christmas? The allure of Christianity rides on the back of a thrice-married billionaire who went bankrupt in the casino business, of all things. Somehow he never learned that casinos don’t make money, they launder it. It’s a big difference. When things eventually go to hell in a handbasket (as they certainly will), which churches are going to get the most credit? If the orange-clown kills millions of people to make a point, who gets the pat on the back? Jesus?
  9. I have sons who have made more money than I ever imagined was possible during those times long ago when I held them as babes in my loving arms. To a man, they think things are just fine. No worries. Yes, health insurance is expensive, but think about one thing for just one minute. (People must know that now is not the time for stupid.) Rich people don’t buy health insurance!  Right? They don’t need it. Anyone who hoards fourteen thousand piles of a million dollars per pile (like the president) doesn’t worry about a $200,000 hospital bill. Billionaires spend more on Rolex watches.

    Video clip of recent Navy UFO sighting here.
  10. During the past week, the media informed the public on three different occasions that at this moment in time when the Russians are dismantling the United States, UFOs scramble over the skies of the world on every continent. Is there anyone out there who hasn’t heard the ominous rumblings of UFOs late at night while they are trying to sleep?
    Since the last news report days ago, not a peep has been heard from the media. Not a line of warning by the replicants who sit in the seats of media-power. They are so life-like, aren’t they? So Perfect. So Desirable. They seem to never mispronounce words or make grammatical errors. Sure, they screw-up. They do.  Listen. Sometimes they say boob-el instead of bubble. That’s how you tell.
    None of this is happening, right? Surely everyone understands by now. It can’t be happening.  Not now.  Not ever.  Cover the eyes, ears, and mouth. Stop screaming.

Why won’t you believe? I’m a pontificator. I’m trying so hard to warn you.


Billy Lee


Two months ago, I discovered QUORA. It’s been around since 2009.

Since 2010, Quora has enabled people to ask experts questions about topics they like; even to answer questions on subjects they claim to know something about.

Quora is a site for geeks and nerds, and so far I  like it. The people who hang out in the areas I hang out tend to be polite, kind, and smart. If they like someone, they follow them and are notified when they post. So far, ten people have signed on to follow me. It’s a start. I think most are from India.

During the first six weeks, 150 or so of my answers were viewed 35,000 times; I got nearly 175 “upvotes”, which enabled many of the answers to move to the head of the line. I wrote most answers in the wee hours between 2 AM and 7 AM when I couldn’t sleep. Insomnia inspired me.

What follows are 25 of the most popular answers I posted to the first 150 or so questions that caught my interest. They are sequenced by popularity—the most read first .

Why not read a few? How many questions can anyone answer? Not many, I’m thinking.

Who knows what you might learn?

What?  You think you know better than a pontificator with no bona-fides? I don’t think so. No way!   😉

1)   What are some of the most popular “mathematically impossible questions“?

Freeman Dyson — one of the longest-lived and most influential physicists and mathematicians of all time — argued that it is impossible to find a whole (or exact) number that is a power of two where someone can reverse its digits to create a whole number that becomes a power of five.

In other words 2^{11} = 2048, right? Reversing the digits to make 8402 does not result in an exact number that is a power of five.

In this case, 8402^{1/5} = 6.09363... plus a lot more decimals. It’s not a whole (or exact) number. Not only that, no matter how many decimal places anyone rounds-off 6.09363... , the rounded number raised to the power of five will never return 8402 exactly.

Dyson claimed that this conjecture must be true, but there is nothing in mathematics that enables anyone to write a proof. He claimed that there must be an infinite number of similar statements—-each one true, none provable.

Click the link below to learn more.


The Snowplow Problem is another “impossible” problem. My differential equations professor assigned it with the promise that anyone who solved it would receive a 4.0 grade, regardless of their performance on tests. I was the only student he ever taught who actually managed it.

The problem goes like this: It is snowing at a constant rate. A snowplow starts plowing snow at noon. By one o’clock the plow has traveled one mile. By two o’clock the plow travels an additional half mile. At what time did it start snowing?

It took me 3 days and two pages of calculations, but I got my 4.0.

Note from the Editorial Board:  Over fifty people on Quora submitted answers to Billy Lee’s Snow Plow problem. One person had the right answer, but would not produce his proof. He did point out an unusual feature of the solution that Billy Lee had not noticed before. Billy Lee characterized the feature as “very surprising.” When pressed Billy Lee refused to reveal its secret. 

2)   How much force is one Newton?

A newton is the force that an average sized apple makes on your hand when you hold it. No matter where in the universe you are; no matter on what planet you stand or how strong the gravitational field, a newton of force always feels the same.

A newton is one kilogram of mass that is accelerating at one meter per second per second. Gravity on earth accelerates everything at nearly 10 meters per second per second. A kilogram of mass feels like 2.2 pounds on earth. One tenth of 2.2 pounds is 0.22 pounds or 3.5 ounces, which is the weight of a typical apple. The weight is the force that you feel against your hand. It is one newton.

On the moon, an object with the mass of a large brick would feel as light as an apple on earth due to the moon’s lower gravity. The force of the brick in your hand would feel like one newton.

3)   x + y = 4 and x^x + y^y = 64 . What are x and y?

The simplest way to solve is to make y = (4-x) and create an equation in terms of x.

An easy version to create and solve is {x^x + (4-x)^{4-x} = 64} . You can solve it by hand using iteration or throw it into an app like Wolfram Alpha and let them solve it in a few seconds.

Either way one value for x is .606098…. The other is 3.393901… , which you can assign to y. The two numbers add to 4.000… and when substituted into both initial equations return the right results.

4)   If I had 1,000,000,000,000,000 times 1,000,000,000,000,000 hamsters floating in space in close proximity, would gravity turn them into a hamster planet?

Assuming the question is serious, it deserves a serious answer.

A typically fat hamster weighs around one ounce, which is about 0.03 kilograms of mass. The number of hamsters in your question is 10E30.

Multiplying the mass of a single hamster by this large number gives the result of 3E28 kilograms.

To compare, the mass of planet Earth is 6E24 kilograms. The mass of the proposed population of hamsters is 5,000 times the mass of the earth.

The sun contains 67 times more mass than the hamster population. If the hamsters are close enough together to hold paws, a hamster planet is almost certain. I haven’t worked out how long the process to congeal would take, but I can estimate that the hamsters would probably die of starvation before the inexorable forces of gravity completed their work.

The hamster planet would be formed mostly from three elements: hydrogen (64%), oxygen (33%), and carbon (10%). 3% would be trace elements like calcium and maybe lithium.

The most likely outcome, given enough time, is a planet-like object. The hamsters have only one-fifth of the mass to make the smallest of the smallest suns — red dwarfs, which populate 67 to 80 percent of the Milky Way Galaxy.

There are way too many hamsters to make a reasonably sized moon.

Their mass (3E28 kg) happens to fall on the border between the range of masses that are required to form celestial objects known as brown dwarfs and the less massive sub-brown dwarfs — sometimes referred to as free-floating planets.

Brown dwarfs don’t have enough mass to ignite like a star, but they do produce heat and can accept small orbiting planets. The chemistry of brown dwarfs is not well-understood and is a bit controversial.

It’s a toss-up, but my vote goes to the notion that the hamsters will eventually form a very large but ordinary planet — a free-floating planet — which I referred to earlier as a sub-brown dwarf. This hamster planet might wander through space for millions (or even billions) of years before being captured by a massive-enough star to begin to orbit.

Because the elements of hydrogen and oxygen are likely to become the constituents of frozen moisture (or water ice), there is the risk that the ice might melt into oceans and perhaps boil away if the hamster planet approaches too close to a star (or sun). In the case where the planet loses its water, a carbon planet with 50 times the mass of earth would form.

Otherwise, should the planet find itself in a far-distant future orbiting in the “goldilocks” zone around a sufficiently massive star, the water would not evaporate. Life could arise in the planet’s oceans. It’s possible.

Life-forms might very well crawl up out of the water and onto land someday where — over the eons and under  ideal conditions — they will evolve into hamsters.

5)   Why is evolution a valid scientific theory despite the fact that it can’t be conclusively proven due to the impossibility of simulating the millions-of-years processes that it entails?

Evolution is a fact that is thoroughly established by observations made in many disciplines of science. Changes in species happen fast or slow; in the lab and in the field.

The mystery is how one-celled life got established so quickly — it was solidly established within one billion years of earth’s formation. It’s taken 3.5 billion years to go from one-celled life to what we have now.

Why so fast to get life started; why so slow to get to human intelligence and civilization?

People have a lot of ideas, but no one is sure. Some life forms have orders of magnitude more DNA than humans. Only 2% of human DNA is used to make the proteins that shape us.

So, yes, there are lots of questions.


6)   Why do cosmologists think a multiverse might exist?

Many high-level, theoretical physicists have written about the obvious problem our universe seems to have, which is that it has too many arbitrary constants that are too tightly constrained to be explained by any theory so far. No natural cause has been found for so many constants, so it’s fertile ground for theorists.

Stephen Hawking, among others, has said that the odds of one universe having the physics that ours has is 1E500 against. He is joking in his English way, because such a large number is essentially an infinity. It’s not possible to constrain a universe like ours by chance unless there are an infinity of choices, and we happen to be in the one that supports intelligent, conscious life.

Two ways of getting to infinity are the concepts of multi-verse and the new one proposed by Paul J. Steinhardt of Princeton University in 2013, which is based on data supplied by the Planck Satellite launched in 2003. Paul is the Einstein Professor of Science at Princeton, so his opinion holds a lot of weight.

Steinhardt has proposed that the universe is ekpyrotic, or cyclic. He has asserted that the universe beats like a heart, expanding and contracting in cycles, with each cycle lasting perhaps a trillion years and repeating, on and on, forever. Each cycle produces conditions — some which are ideal for life. This heart has been beating forever and will continue to do so, forever.

Conscious Life

7)   How will we visit distant galaxies if we cannot travel faster than light? 

We will never visit distant galaxies, because they are too far away; most are moving away from us faster than our current technologies can overtake. At huge distances space itself is expanding, which adds to our problems.

The expansion of space is gradually accelerating. Any increase in performance by space vehicles over the next few thousand years is certain to be overwhelmed by the accelerating expansion of the universe.

As time goes on the amount of objects that are reachable (or even viewable) by earthlings will shrink.

On the happy side, our own solar system has at least 165 interesting places to visit that should keep folks fascinated for many thousands of years. A huge cavern has been discovered on Mars, for example, that might make a safe habitat against some forms of radiation dangers; it seems to be a place where a colony of humans might be able to live, work, and survive — perhaps even flourish.

Elon Musk is planning a mission to Mars soon.

8)   What is the mathematical proof for a+a = 2a ?

Some things that are true can’t be proved. All math systems are based on axioms, which are statements believed to be true but which, in themselves, are not provable.

This link provides a list of axioms for addition:

A lot of interesting philosophical and mathematical work has been done on conjectures that are believed to be true, but can’t be proved.


9)   Can you explain renormalization in physics in simple words?

There is a problem in physics that has to do with the huge variation in scales between the very large and the very small. This problem of scales involves not only the size and mass of things, but also forces and interactions.

Philosopher Robert Pirsig believed that the number of possible explanations that scientists could invent for phenomenon were, in actual fact, unlimited.

Despite all the math and all the convolutions of math, Pirsig believed that something mysterious and intangible like quality or morality guided our explanations of the world. It drove him insane, at least in the years before he wrote his classic book, Zen and the Art of Motorcycle Maintenance.

Anyway, the newest generation of scientists aren’t embarrassed by anomalies. They have taught themselves to “shut up and calculate.” The digital somersaults they must perform to validate their work are impossible for average people to understand, much less perform. Researchers determine scales, introduce “cut-offs“, and extract the appropriate physics to make suitable matches to their experimental results.

The tricks used by physicists to zero in on pieces of a problem where sensible answers can be found have many names, but renormalization is one of the best known.

When physicists renormalize an equation, they cut away infinities and other annoying problems (like dividing by zero). They focus the range of their attention to smaller spaces where the vast differences in scales and forces don’t blow up their formulas and disrupt putative pairings of their carefully crafted mathematics to the world of actual observations.

It’s possible that the brains of humans, which use language and mathematics to ponder and explain the world, are insufficiently structured to model the complexities of the universe. We aren’t hard wired with enough power to create the algorithms for ultimate understanding.


10)   If a propeller rotates at the speed of light at half of its length, what happens to the outer parts?

Only the ends of the propeller can rotate at near light speed (in theory). At half lengths the speed of the propellers will be half the speed of their ends, because the circumference of a circle is 2πr. (There is no squared term.)

So the question is: will the propellers deform according to the rules of the Lorentz transformation along their lengths due to the difference in velocity along their lengths?

The answer is, yes.

As you move outward along the propeller, it will become thinner in the direction of rotation, and it will get more massive. A watch will tick more slowly at the end than at the middle.

I am not sure how it would look to an outside observer. Maybe such a propeller would resemble in some ways the spiral galaxies, which don’t rotate the way we think they should. Dark matter and energy are the usual postulates for their anomalous rotations. Maybe their shape and motion is related to relativity in some way. I really don’t know.

In reality, no propeller can be constructed that would survive the experiment you describe. But in theory (and ignoring the physical limitations of materials) there would be consequences.

However, no part of the propeller will move at light speed or higher. Such speeds for objects with mass are impossible.

11)   What is the fundamental concept behind logarithms?

The first thing that anyone might try to understand is that the word logarithm means exponent.

Example 1:

log 100 = 2 . What does this expression say? It says that the exponent that makes 100 is 2. What confuses people is this: exponent acting on what number?

The exponent acts on a number called the base. Unfortunately, the base is not written down in the two most common logarithm systems, which are log and ln.

The base for the log system is 10. In the example above, the exponent 2 acts on the base 10, which is not shown. In other words, 10^2 = 100 , right? The exponent that makes 100 from the base 10 (not shown) is (equals) 2.

Example 2:

ln 10 = 2.302585… .  What does this expression say? It says that the exponent that makes 10 is 2.302585… . Again, exponent acting on what number?

The base used in the ln system is 2.7182818… ,which is an irrational number that has an infinite number of decimal places. It happens to be a useful number in all branches of science and math including statistics, so mathematicians have decided to represent this difficult-to-write-down number with the letter “e”, which is known as Euler’s number.

The base for the ln system is e . In the example above, the exponent 2.302585… acts on the base e , which is not shown. In other words, e^{2.302585...} = 10 , right? The exponent on e ( which is 2.7182818… and not shown in the original equation above) that makes 10 is (equals) 2.302585… .

All other logarithmic systems express the base as a subscript to the right of the word log.

Example 3:

log_{7}49 = 2 . This expression says: The exponent on seven that makes 49 equals 2.

12)   Why do so many spiritual types have mental blocks about science and mathematics?

Everyone has mental blocks about science and math including scientists and mathematicians. Like the old song, people hear what they want to hear and disregard the rest. Einstein never accepted most of quantum physics even after it was well established and no longer controversial.

People don’t like the feeling of “cognitive dissonance”. The tension between strongly held beliefs and objective facts can bring unbearable psychological pain to most people. Someone once said that genius is the ability to hold contradictory ideas inside the mind. Most people don’t do that well; they don’t like contradictions.

Here is a link to an essay called Truth that some will find interesting:


13)   Is time infinitely divisible?

Einstein said that time and space (i.e. space-time) depends on mass and energy, which are equivalent. In the absence of mass and energy, space and time are meaningless.

The most recent experiments by NASA have found no evidence that time is anything but continuous. However, the shortest time possible is the length of time it takes light to move the shortest distance possible, which is called Planck time. It is thought to be 5.39E-44 seconds.

Time can be divided into as many smaller increments as anyone wants, but nothing can happen in fewer than the number of intervals that add to 5.39E-44 seconds. Time is a variable that isn’t fundamental. It expands and shrinks in the presence of mass and energy.

Some physicists of the past suggested that the “chronon” might be the shortest interval of time. It is the time light travels past the radius of a classical (at rest) electron — an interval of 6.27E-24 seconds. Its calculation depends only on mass and charge, which can change if a particle other than an “at rest” electron is measured.

It seems to me that time is probably best thought of as being continuous. That said, it doesn’t mean that mass-energy interplay isn’t pixelated — much like a digital camera image. Pixelation is critical to a conjecture concerning the preponderance of matter over anti-matter — a conjecture described in the essay CONSCIOUS LIFE.

14)   Which is bigger:  \frac{3}{5} or \frac{1}{9} ?

Think of fractions as pies which are all the same size. The bottom number is the total number of pieces each pie is cut into. The first pie was cut into 5 pieces, which are all the same size. The second pie was cut into 9 pieces which again are all the same size.

The second pie is cut into smaller pieces than the first pie, because there are more pieces. Right?

Mice come along and eat pieces from both pies. The top number is the number of pieces they left behind; the top number is the number of pieces the mice didn’t eat.

So which pie plate has more pie on it? Is it the 5 piece pie that has 3 pieces left or the 9 piece pie that has 1 piece left?

If you think hard you will figure out that it must be the first plate that has the most pie on it. Right?  

15)   Why is a third of 30 equal to 10 and not 9.999999999, as a third of 10 is 3.33333333? 

You can make three piles of ten objects in each pile. When you count the total, it adds to exactly 30 objects. So the answer of “10” is demonstrably true, right? Three piles of ten adds to thirty.

There is no way to make three piles of any identical objects that adds to 10. Three piles of three adds to nine. Four piles of three objects adds to twelve.

We are required to make three piles of three objects and then add a piece of a fourth object to each pile that is smaller than a whole piece.

It turns out that the fourth object is 1/3 of a whole object. When these three piles of three objects plus 1/3 of an object are added up they equal exactly ten.

The problem in understanding comes from trying to grasp that 1/3 — when written as a decimal — is what mathematicians call a repeating decimal. The rules of arithmetic say that the decimal form of 1/3 is calculated by dividing “1” by “3”.

Following the rules of arithmetic when doing the division forces an answer to the problem that results in a repeating decimal — in this case, 0.333333… .

There is no way around these rules that keeps math working right, consistent, and accurate.


16)   Will we be able to have life extension through cloning? 

Cloning not only doesn’t work, it can’t work.

That said, the idea of cloning is to make a genetic replicant of an existing life-form. Extending life-span would require changes to the genome through other means involving changes to structures called telomeres, probably, which straddle the ends of chromosomes in eukaryotic cells. Here is a link:  Telomere

A short discussion of cloning is included in the essay at this link:  NO CODE

No Code is long (8,500 words), but explains in words, pics, graphics, videos, and links some of the complexities, misunderstandings, and dangers of current genetic-engineering in language suitable for undergraduates. It explains basic cell biology, protein production, and much more.

17)   Why does time slow down when we are on a massive planet or star like Jupiter? 

Gravity is equivalent to acceleration. Accelerating clocks tick slower, according to General Relativity, which has been confirmed by experiments. It has to do with the concept of space-time and the fact that all objects travel through space-time at the same rate.

To understand, it helps to read up on space-time, special relativity, and general relativity. The concepts aren’t easy. The universe is an odd place, but it can be described to a somewhat fair degree by mathematics.

Some of the underlying reasons for why things are the way they are seem to be unknowable.

18)   If the ancients had focused on science instead of religion, could we have become immortal by now? 

Immortality is not possible due to the odds of accidental death, which at the current rate makes death by age 25,000 a virtual certainty for individuals.

Worse: the odds for extinction of the human species as a whole is much higher — it’s a statistical certainty for annihilation within the next 10,000 years according to experts. It seems counterintuitive, but it’s true.


19)    How do I solve, if the temperature is given by f(x,y,z) = 3x^2 - 5y^2 + 2z^2 and you are located at (\frac{1}{3} , \frac{1}{5} , \frac{1}{2}) and want to get as cool as possible, in which direction should you set out? 

 You want to establish what the gradient is, establish its direction, then head in the opposite direction, right?

By partial differentiation the gradient is (6x – 10y + 4z), right? You don’t have to take another partial derivative and set it equal to zero to establish a maximum, because all the second derivatives of the variables are equal to one, right? You can drop the variables out and treat them as unit vectors like i, j, & k, correct?

The resulting vector points in the direction of increasing temperature, right?

Changing the signs makes a vector that points in the opposite direction toward cooler temperatures, correct? That vector is (-6, 10, -4).

The polar angle (θ) is 71.068 degrees and the azimuth angle (φ) is 120.964 degrees. The length (or magnitude) is 12.3288. Right? (We won’t use this information to solve the problem, but I wanted to write it down should I need to refer to it to respond to any comments or to help check my work graphically.)

These directions are from the origin, and you aren’t located at the origin. To determine the direction to travel to get to (-6, 10, -4), you need to subtract your current position. Again, for reference your location is .6333 from the origin at θ = 37.8636 degrees and φ = 30.9638 degrees. Right?

After subtracting your position vector from the gradient vector, the resulting vector is (-6.333, 9.8, -4.5). Agree?

This vector tells you to travel 12.506 at a polar angle (θ) of 68.9105 degrees and an azimuth angle (φ) of 122.873 degrees to intersect the gradient vector. At the intersection you must change direction to follow the gradient vector’s direction to move toward cooler temperatures at the fastest rate.

I haven’t graphed out the solution to double-check its accuracy. You might want to do this and let me know if you agree or not.

20)   What is \sqrt[3]{i} - \sqrt[3]{i} equal to?

The answer is zero, of course.

But not really. It only seems that way. Each number has three roots.

Depending on which roots are chosen the result can be one of six different sums (as well as zero if both roots are the same). We have to start somewhere so:

What is i^\frac{1}{3} ?

i = e^\frac{{i\pi}}{2} .  Right?

Therefore, a third root of i is e^\frac{{i\pi}}{6} .  Right? It’s not the only root.

It’s the principal root. There are three third roots, which are equally spaced around the unit circle. Right?

It’s clear by inspection that to be equally distributed around the unit circle the other two roots must be e^\frac{{i5\pi}}{6} and -i.  Right?

Convert the three roots to rectangular coordinates and do the subtractions.

Here are the roots in rectangular form: (.86603 + .50000 i) , (-.86603 + .50000 i) , and (0.00000 -i).

Here are the six answers (in bold type) to the original question with the subtractions shown to the right:

1.7302 = (.86603 + .50000 i) – (-.86603 + .50000 i)

(.86603 +1.5 i) = (.86603 + .50000 i) – (0.00000 -i)

-1.7302 = (-.86603 + .50000 i) – (.86603 + .50000 i)

(-.86603 + 1.5 i) = (-.86603 + .50000 i) – (0.00000 -i)

(-.86603 – 1.5 i) = (0.00000 -i) – (.86603 + .50000 i)

(.86603 – 1.5 i) = (0.00000 -i) – (-.86603 + .50000 i)

These rectangular coordinates can be converted back to the Euler-form (e^{i\theta} ).  It’s easy, if you know how to work with complex variables. In Euler-form the angle in radians sits next to i.  The angle directs you to where the result lies on the unit circle. Right?

As mentioned earlier, if both roots are chosen to be the same, then in that particular case the result is zero.

21)   What is tensor analysis and how is it used in physics?

Understanding tensors is crucial to understanding Einstein’s General Theory of Relativity.

This question seems to assume that everyone knows what tensors are and how they are represented symbolically. I am guessing that some folks reading this question might want some basics to better understand the explanations of how tensors are used for analysis in physics.

If so, here are links to two videos that together will help with the basics:

22)   What is the velocity of an electron?

Electrons can move at any speed less than light depending on the strength of the electro-magnetic field that is acting on them. Inside atoms electrons seem to move around at about one-tenth of the speed of light. You might want to check me on this number. The situation is as complicated as your mind is capable of grasping.

When interacting with photons of light electrons inside atoms seem to jump into higher or lower shells or orbits instantaneously. That said, it is impossible to directly observe electrons inside atoms.

On an electrical conductor like a wire, electrons move very slowly, but they bump into one another like billiard balls or dominoes. The speed of falling dominoes can be very high compared to the speed of an individual domino, right?

So the answer is: it all depends…

23)   What exactly is space-time? Is it something we can touch? How does it bend and interact with mass? 

Space-time, according to Einstein, depends on mass and energy for its existence. In the absence of mass and energy (which are equivalent), space-time disappears.

The energy of things like bosons of light, which have no mass, is proportional to the frequencies of phenomena called electric and magnetic fields. Small packets of these oscillations are called photons.

Many kinds of oscillating fields like the electro-magnetism of light permeate (or fill) the universe. In this sense, there is no such place as nothing in the universe anywhere at any scale.

The instruments and tools of science (including mathematics) can give a misleading impression that at very small scales massive particles exist.

According to John Wheeler, mass at small scales is an illusion created by our interaction with measuring devices and sensors.

Mass is a macroscopic statistical process created by accumulations of whatever it is that exists at the very deep bottom of a reality to which we have yet to gain access. These accumulations are visible to humans; they span 46 billion light years in all directions from the vantage-point of Earth and are collected for the most part in more than one-trillion galaxies, according to the latest satellite data by NASA.

Mass interacts with everything that can be measured (including everything in the Standard Model) by changing its acceleration, which is equivalent to changing its momentum. Energy changes the momentum of everything in the Standard Model as well.

It is in this sense that mass and energy are equivalent. It is in this sense that space-time depends on mass and energy. Space-time does not act on mass and energy; it is its result.

Space-time is a concept (or model) that for Einstein at least helped him to quantify how mass and energy behave on large scales. It helped him to explain why his idea that the universe looks and behaves differently to observers in different reference frames might in fact be the way the universe on the largest of scales really works. It helped him to describe a geometric explanation for gravity that many people find compelling.


24)   Hypothetically speaking, if one could travel faster than light, would that mean you would always live in the dark?

The space in which objects in the universe swim does expand faster than light when the expansion is measured over very large distances that are measured in light-years. A light year is six trillion miles.

At distances of billions of light years the expansion of space between objects becomes dramatic enough that light begins to stretch itself out. This stretching lengthens the distance between the peaks and valleys of the electric and magnetic waves that light is made from, so its frequency drops.

The frequencies in white light can stretch so dramatically that the light begins to appear red. It’s called red-shift.

Measuring red-shift of star-light is a way to tell how far away an object like a star is. As light stretches over farther distances we lose the ability to see it.

The frequencies stretch into infra-red waves (called heat waves) and then at even farther distances stretch to very long waves called radio-waves. Special telescopes must be placed into outer-space to see these waves of light, because heat and radio waves radiating from the earth interfere with instruments placed at the earth’s surface.

Eventually the distances become so great that the amplitudes (or heights) of the waves flat-line. They flat-line because space is expanding so fast that light can’t keep up. Light loses its structure. At this distance the galaxies and stars drop out of the sight of our eyes and even our sensors and instruments. It’s a horizon beyond which the universe is not observable.

No one knows how big the universe is, because no one can see to its end. The expansion of space —  tiny over short distances — starts to get huge at distances over 10 billion light years or so. The simple, uncomplicated answer is that the lights go out at about 14.3 billion light years.

Over the next few billion years the universe we can see will get smaller, because the expansion of space is accelerating. The sphere of viewable objects is going to shrink. The expansion of space is speeding up.

The problem will be that the nearby stars that we will always be able to see (because they are close) are going to burn out over time, so the night sky is going to get darker.

Most (4 out of 5) stars in our galaxy are red dwarfs that will live pretty much forever, but we can’t see them now, so we won’t be able to see them billions of years from now either. They radiate in the infra-red, which can only be seen with special instruments from a vantage point above our atmosphere.

Stars like our sun will live another 4 or 5 billion years and then die. The not too distant future of the ageless (it seems) universe is going to fall dark to any species that might survive long enough to witness it.

25)   What does “e” mean in a calculator? 

There are two “e”s on a calculator: little “e” and big “E”.

Little “e” is a number. The number has a lot of decimals places (it has an infinite number of them), so the number is called “e” to make it quick to write down.

The number is 2.71828… . The number is used a lot in mathematics and in every field of science and statistics. One reason it is useful is because derivatives and integrals of functions formed from its powers are easy to compute.

Big “E” is not a number. It stands for the word “exponent”, but it is used to specify how many places to the right to move the decimal point of the number that comes before it.

5E6 is the number 5,000,000, for example. The way to say the number is, “five times ten raised to the sixth power”. It’s basically a form of shorthand that means 5 multiplied by 10^6 .

Sometimes the number after E can be negative. 5E-6 would then specify how many places to the left to move the decimal point. In this case the number is 0.000005, which is 5 multiplied by 10^-6 .

Bonus Question:  What difficulties lie in finding particles smaller than quarks, and in theory, what are possible solutions? 

The Standard Model is complete as far as it goes. Unfortunately, it covers only 5% of the matter and energy believed to exist in the universe.

And humans can only see 10% of the 5% that’s out there. We are blind to 99.5% of the universe. We can’t see energy, and we can’t see most stars, because they radiate in the infra-red, which is invisible to us.

The Standard Model doesn’t explain why anti-matter is missing. It doesn’t explain dark matter and energy, which make up the majority of the material and energy in the universe. It doesn’t explain the accelerating expansion of the universe.

Probing matter smaller than quarks may require CERN-like facilities the size of our solar system, or if we’re unlucky, larger still.

We are approaching the edge of what we can explore experimentally at the limits of the very small. Some theorists hope that mathematics will somehow lead to knowledge that can be confirmed by theory alone, without experimental confirmation.

I’m not so sure.

The link below will direct readers to an essay about the problem of the very small.


Bonus Question 2 – What if science and wisdom reached a point of absolute knowledge of everything in the universe, how would this affect humanity?   

Humanity has reached a tipping point where more knowledge increases dramatically the odds against species survival. Absolute knowledge will result in absolute assurance of self-destruction.

Astronomers have not yet detected advanced civilizations. The chances are excellent that they never will.

Humans are fast approaching an asymptotic limit to knowledge, which when reached will bring catastrophe — as it apparently has to all life that has gone before in other parts of the universe.

Everywhere we look in the universe the tell-tale signatures of advanced civilizations are missing.


We hope readers enjoyed these questions. Follow Billy Lee on Quora where you will find answers to thousands of unusual and interesting questions on every subject imaginable.  The Editorial Board  

If it don’t roast, I don’t post.

Billy Lee


Fundamentalist Christians have the reputation for carte blanche support of everything Israel. Many citizens of Israel hold dual citizenship inside the United States. The third director of Homeland Security, Michael Chertoff, is a dual citizen.

It’s not unusual. The current acting director, Elaine Duke, is the grandchild of Sicilian immigrants. Everyone in America comes from somewhere. Divided loyalties are as American as gluten-free apple pie. 

I mention it because since 2006 when George W. Bush was president, the Secretary of Homeland Security joined those in the line of succession. The line of succession is now seventeen names long. None are Democrats. Not right now. A few are independents like General Mattis, the Secretary of Defense. 

Acting Secretary of Homeland Security, Elaine Duke. She is last in line to be president.

The Homeland Security Director is dead last on the list. The current acting director, Elaine Duke, is (in my humble opinion) the only person in the group who is actually qualified to be president. The list includes names like Steven Mnuchin, Betsy DeVos, and Ben Carson. Some on the list form a kind of rogue’s gallery of characters that could conceivably populate the cast of the classic, One Flew Over the Cuckoo’s Nest. 

The USA’s crazy-Christian, comb-over president leads the list; he directs the country; he is on the top of the world. Like 81% of the fundamentalists who elected him, he is all-in for Israel. Whoever robs and kills in defense of Israel is fine with fundamentalists. They never criticize Israel, even in love. It doesn’t happen. 

The president says that he is moving our embassy to Jerusalem. He lies a lot, so who knows? According to him, Jerusalem is now the exclusive capital of Israel; it is no longer shared with Palestine—no matter what modern history and world opinion have to say.

The USA has the power to make truth and justice on the ground whatever it wants it to be. No need for negotiation. No reason to compromise. And by the way, settlements built on land confiscated from losers are just fine, no problems. Come on. Moral qualms? You’re kidding, right? 

Never mind that the Old City center of Jerusalem is segregated into quarters controlled and lived in by Armenians, Christians, Muslims, and Jews. Never mind that the modern city is much larger; that nearly 40% of the population is Arab; that holy sites of all faiths abound.

The borders of biblical Israel and all the territories within are going to be re-established, just as they were three thousand years ago by God Himself. There is nothing to negotiate. No compromises will be necessary. Thank you very much. 

Christians support Israel, because they believe God has a covenant with modern-day Israel validated by words written in the book of Exodus thousands of years ago. The United States and Israel are joined at the hip like Siamese twins on this one. Israel might as well be added to the collection of fifty states that make the USA.

The reality, though, is that Israel is more like Washington DC. It’s not really a state—it’s a country, obviously—but it has influence on America beyond its size by half. What goes on in Israel affects the United States in big ways (or bigly, as the president likes to say).

Israel is the size of Chicago and its suburbs and has about the same population. Right? Its grip on the United States is vice-like. It rides the U.S. shark like a remora fish. Without its shark for protection, the remora fish gets eaten, like any other small fish in a big ocean. It must be protected.

I’m totally on board. Israel has enemies. The generation that parented the Jewish people who live in Israel today were nearly exterminated by Hitler. The post World War refusal of the west to take in refugees added to their determination to go home to their ancestral lands.

The problem was that people already lived in Israel and had for centuries. Despite the good faith efforts of the nations to broker peace and safety, every Arab neighbor attacked Israel on the day of its rebirth.

Israel won the military contest and occupied lands that international agreements said they had no right to hold. Refugees who had crossed the Jordan River to escape the conflict couldn’t come back. Israel locked them out. It now had a Palestinian problem that would never be solved.

Trust on both sides evaporated. The world today lives with the dangers, resentments, and hatreds that erupted from a failure to love one another during the years when it mattered most.

The Dome of the Rock is controversial within Israel and Palestine. Eighty kilograms of gold leaf cover the dome. At today’s close, the gold’s value is $3,600,307.60. The former King Hussein of Jordan sold one of his London homes in 1993 to raise the money. He died on February 7, 1999 at age 63 from complications of cancer. 

The world owes the Jewish people a safe place to live. They have suffered enough. In the meantime, we need to build a fairer world. Jews, despite the horrors they have endured, do not have a monopoly on suffering. Many people, including Palestinians, have gotten a raw deal. It’s time to set things right.

I don’t see fundamentalist Christians as being helpful. I’m not feeling the love. I’m not seeing an effort to understand that God loves people who are everywhere. People who God loves are sprinkled like salt among the Palestinians and the Jews of Israel.

These are the people that Christ Jesus gave his life to save. I’m not feeling the respect for Christ’s vision from the fundamentalists who right now have an opportunity to comfort the fearful and dispossessed on all sides. All sides. Believe it.

For Jewish people the stakes are particularly high given a history that repeatedly shows that when they don’t have safe haven, haters attack them. The United States and France can be safe places for the most part, but Israel is special. Israel is an established safe haven for Jews, period. They need one. The world, through the United Nations, established it. A lot of history backs the decision to help, some of it recorded in the Bible.

That said, no follower of Christ Jesus, no one who has read the Bible—New Testament, the Torah, the Prophets—believes that Israel was chosen by God to rule the world. I don’t have to quote the Bible. People know what the Lord requires. He asks people to love mercy, act justly, and walk humbly with their Creator. Does anyone believe it? 

Jesus didn’t immolate himself on a Roman cross because people are good, but because they are wicked. People chosen by Jesus don’t rule; they give up everything they have to serve and love others. It’s simple, really.

It’s not easy. Some say it’s impossible apart from the kind of love that was shown to us by a messiah who suffered.

When I studied Hebrew at a local Hillel school many years ago, a girl in the class actually said that Jews were chosen by God to rule the world. Israel would save the earth and bring light to dark. The rabbi nodded his assent. I asked what she thought about the concept of forgiveness. The rabbi waved his hand, and the group moved on.  

After class, the teacher pulled me aside. Grace is a Christian concept, he told me. Grace has no place in Judaism. 

The instructor locked eyes with me and explained in no uncertain terms that a fundamental tenet of my faith was crap. He intended to make an impression, and he succeeded.   

At about the same time a geneticist and his wife came from Israel to America to study at a nearby university. They had young kids the same age as mine. Somehow we met and liked each other. They became close friends. We visited their apartment from time to time. I noticed that they read the Bible to their children, so I asked about it. It’s our history, Yossi explained. We are atheists. But our children must learn who they are. 

A few months later we attended a summer dinner at a kiva on campus where a Jewish writer gave a short talk on Israel. We dressed-up and took the kids. Yossi, his family, and mine walked together on the pathway that led to the building.

I was surprised to learn that to get into the event we had to make our way past a line of about a hundred Palestinian demonstrators. It was like walking a gauntlet.

The protestors held signs, but the odd thing was they didn’t speak. They stayed quiet. It was eerie. More than a few wore ski-masks. They stared through eye-holes in silence. No smiles. I felt afraid. My stomach churned. I smelled fear in my nostrils, but Yossi seemed unfazed. I reached for my children and held their hands.

Weeks later, Yossi brought his family to visit at my place. To make polite conversation I asked Yehudith, his wife, about life in Israel. What was it like living there? She said that she didn’t want to go back. The air-raid sirens in Israel frightened her. When they wailed during the day they triggered panic attacks.

Yehudith and her husband were Sabras—native born Israelis. Born and raised in Jerusalem, they didn’t travel, because they had no money.

They knew no other life. I too was poor then. I was raising two children by myself and living in a small house. It was a thousand-square-feet with an unfinished basement. When Yossi and Yehudith first visited they said it must be a mansion. Yehudith marveled at its size and amenities.

She couldn’t believe how well-off we were. She marveled at how much stuff we had. She gasped at the size of our yard. In Jerusalem people didn’t have yards.

Yes, we did have a big yard. No one nearby had one that came close. It was lush and green. Its size was an accident of good fortune—the result of bad planning by developers.

I decided not to tell Yehudith that we were poor. I didn’t have it in me to make her feel worse. She wasn’t going to believe it anyway. 

Billy Lee 


While the Little Rocket Man and North Korea capture the world’s attention, our president is in Tokyo to deal with a threat that dwarfs anything we have faced since the Japanese attack on Pearl Harbor 76 years ago.

The surprise attack against our Navy on Sunday morning, 7 December 1941, started a cascade of retaliation against the Japanese that three-and-a-half years later resulted in 67 Japanese cities burnt to ashes during a few months of sustained “fire-jelly” attacks by hundreds of Boeing-29 Superfortress bombers and other aircraft. After napalming the cities to dust, the United States followed the horror with a “preemptive” nuclear strike against the cities of Nagasaki and Hiroshima.

Nine million Japanese civilians were left homeless. The death toll has never been definitively calculated, but two million souls is a reasonable guess.

The distance from Pyongyang, North Korea to Tokyo, Japan is 800 miles; to Hawaii, 4,400 miles; to Los Angeles, 6,000 miles; to Seattle, 5,150 miles; to Alaska, 3,200 miles. The border of North Korea meanders 25 to 50 miles from downtown Seoul, South Korea.

A few years after the stalemate of the Korean War, General Curtis LeMay—head of Strategic Air Command—claimed that his pilots had killed a similar number of Koreans by aerial bombardment—20% of the population.

The United States killed an estimated million Iraqi civilians in the more recent wars in the Middle East, which included the Gulf War and the Iraq War.

It killed two million Vietnamese civilians during the Vietnam genocide of the 1960s and 70s.

In August 1945, USA bombers killed hundreds of thousands of Japanese civilians in atomic bomb attacks on Hiroshima and Nagasaki. Millions were burned alive in fire-jelly (napalm) bombings, which decimated 67 cities over several months. Evacuation of cities helped to reduce casualties. 

Why am I bringing up a bunch of disturbing statistics? What’s the point? Why not leave unpleasant memories forgotten in a distant past where they can’t impact the happy lives we live now, not then?

What possible benefit can remembering the past confer upon our contented present? Why bother puking up a sour history that only the old-timers among us experienced? 

May I ask one more question? Maybe thinking about the answer will help some to make sense of current events that seem to have no rhyme or reason.

Of the fifty countries against which we have directed our military wrath since World War II, which among them has a right to the biggest grievance? Who did we hurt the most? 

Which country has been forced to endure the shame of a military occupation that never ends? Ok, maybe it sounds like more than one question. Deal with it. 

America fights secret and not so secret wars against communist, Islamic, western hemispheric, and, it turns out, African countries all the time. We have conducted strategic operations against friend and foe alike since World War II.

We have meddled in the internal politics of super powers like Russia and China. The Dalai Lama of Tibet wrote in his book Freedom in Exile that the United States gave him millions of dollars to incite violence against China, for example.

The USA has attacked militarily one in four of the 190 countries on the earth during the modern era. Which country is the one most likely to harbor a secret ambition for revenge?

America keeps itself in a state of perpetual war to feed the appetites of voracious weapons manufacturers whose stockholders are among the world’s most affluent. The AUMF (Authorization for the Use of Military Force against terrorists) passed Congress, and President Bush signed the bill in August 2001 for a reason—to fuel the demands of arms dealers to free them from the inconvenience of securing approval by Congress to declare wars—which the Constitution demands. Only Barbara Lee (no relation to Billy Lee) of California voted against it.

Since 1991 Congress has passed and the president signed four AUMFs, mostly to cut down on the amount of work and resulting delays that are inevitable when large elected groups of representatives are compelled to go on record for or against any particular conflict. 

We in America live under a lot of illusions. We tell ourselves a lot of lies about how wonderful we are and how everyone wants to be like us. Our enemies who fear us the most insist—some of them anyway—that they love us; they want to live with us and be like us, and we tend to believe them.

No one tells a command officer who is carrying an automatic assault rifle that he is a pig; the term “butt-wipe” is never used. No one wants to die for a no good reason like name calling, for example. Our subjugates place flowers in the barrels of our guns and tell us they love us.

Everyone who has been shamed and humiliated prays for their day of liberation; the day of their revenge; the day the world is finally set right. It’s human nature. The desire to settle scores crosses cultural, religious, and geographical boundaries.

Few countries that have suffered cremation by fire of millions of their citizens forget. They don’t forgive. Think long and hard. It’s true.

For almost a year Billy Lee lived where he could view Mount Fuji from his bedroom window during his two-year stay in Japan. The Editorial Board

The situation in Japan is dire; it really is. The United States for some insane and goofy reason permitted the Japanese over the past thirty years to build the most sophisticated nuclear power grid the world has ever seen.

The USA sold the Japanese uranium-impregnated fuel rods. A by-product of their use (to produce the intense heat required to generate electricity) is plutonium. Instead of collecting and disposing the spent fuel rods, the Japanese built facilities to extract the plutonium. They promised to use the plutonium for fuel in advanced power generators called “fast reactors.” Fast reactors are, in theory, cheaper and less complicated; they are also more volatile; more dangerous to operate. 

After the earthquake and tsunami of 2011, the Japanese abandoned “fast reactors”. They discovered during the audits they conducted following the disasters at Fukushima and other facilities that their fast reactors had safety records that bordered on terrifying. They stopped using plutonium for fuel. With no place to “burn” the plutonium they were harvesting, it began to accumulate, bigly.

In the entire universe plutonium is found above trace amounts at one location and one location only: planet Earth. Plutonium went extinct due to radioactive decay billions of years ago. It can be created during rare cosmic events, but the bomb-making kind—Pu 239—is a manufactured element that does not occur in nature. It is a by-product of nuclear fission reactions. It hides itself within the matrix of elements that make up the remnants of spent fuel rods.

Plutonium is among the most poisonous substances known. The speck of plutonium dust that kills you, you will likely never see. Some scientists today have downplayed the lethality of plutonium 239. My advice is to be skeptical whenever vast amounts of money and power fuel a controversy.

Regardless of its lethality as a poison, no one argues that fourteen pounds is enough plutonium to make an atomic bomb of a construction so unsophisticated that a high schooler could fashion the necessary components in shop class. Sophisticated bombs require even less plutonium—a mere nine pounds.

This is what plutonium powder looks like. Japan has 94,000 pounds of it. 14 pounds are required for an unsophisticated bomb; 9 pounds for a sophisticated version.

Japan has harvested 47 tons (94,000 pounds) of high-grade plutonium from its nearly one-hundred or so nuclear power and processing plants, which include power plants, research reactors, fast reactors, reprocessing installations, and recently decommissioned facilities—decommissioned due mostly to safety concerns.

Japan’s production schedule is running at a frenetic pace—adding eight tons of surplus plutonium to its stockpile every year into the foreseeable future unless the United States is able to shut down Japan’s reprocessing installations with an agreement scheduled for negotiation in 2018. Our new president has said the old agreements won’t be changed.

By this time next year the Japanese will have accumulated enough high-grade Pu 239 to make as many as 12,000 atomic bombs. Should it make that choice, Japan will possess the world’s largest nuclear arsenal.

Plutonium is heavy. Nine pounds of Pu 239 is the size of a softball. It is exactly the right size to construct a single atomic bomb. By this time next year Japan will possess enough Pu 239 to make 12,000 bombs.

What follows next in this essay is the scary part. Some readers might want to bail and maybe find a good comic book to occupy their imaginations.

Despite agreements with the United States that followed World War II, Japan has one of the largest military budgets in the world. The country spends 42 billion dollars per year on its military. This expenditure does not include its civilian nuclear power system or its civilian space exploration programs. 

The Japanese consolidated three civilian rocket launching companies into one (named JAXA) in 2003. They are launching rockets into space all the time. JAXA designed, built, launched, and maintains the largest module on the International Space Station. The Japanese have spacecraft in the asteroid belt and spy satellites in earth orbit. These are civilian programs. 

Although the military budget of the United States seems huge, people might want to consider that the USA spends one-third of its military dollars on salaries and pensions. No other military spends as much. It maintains 800 military bases in 70 countries at an expense of $200 billion—an expense that other militaries simply don’t have. Japan spends about the same amount on defense as England, France, and Germany. A controversial argument can be made that the combined military might of Russia, China, Japan, and North Korea exceeds that of the United States. It is an argument that is hard to prove, because countries lie about their military expenditures, war-fighting readiness, and technical capabilities. The chart above is misleading in another important way, because it doesn’t include expenditures on nuclear weapons—their production, maintenance, and modernization—which are state secrets in all the countries that possess them.  

The Japanese don’t have to make bombs from their plutonium stores to wreak havoc on an adversary. They can pulverize the metal into aerosols and release plutonium dust into the air over cities.

They can load plutonium into drone subs like rumors say the Russians have done and set hundreds of them in the coastal waters of our country. The subs can lie in ocean sand and silt for decades before releasing their poisons, should it ever become necessary.

Their advanced missile technology might enable Japan to overwhelm our defenses by launching multiple warhead missiles over our homeland. It might take a few months, but poisoned populations would eventually succumb to the release of toxic dust.

And, should they choose to make bombs, well, any country with the resources of a country as sophisticated as Japan can turn high-grade plutonium into bombs in a few days; they can possess the capability to create hell on earth in the blink of an eye, anytime they choose. With the right (or wrong) leadership they can unleash a nightmare of suffering far worse than the inferno we inflicted on them 72 years ago.

This plant is the place where the Japanese extract plutonium from spent nuclear fuel rods. The Japanese have admitted on NHK television that they have 94,000 pounds of plutonium that they have no use for nor any place to safely store.

Plutonium is an artificially produced killing material that no human being, company, or country should ever be allowed to possess or use. It is a forbidden apple of physics that can only bring anguish to whoever uses or shares it with others. 

Japan has the potential to threaten the world with the same level of terror as the United States, Russia, China, Pakistan, India, Britain, France, Germany, Israel, and who knows what other countries. Many countries are conducting (in secret) diabolical engineering even now and will continue to do so into the foreseeable future.

What could be worse? Believe it or not, our predicament might already be much worse than anyone in the USA is willing to think about or imagine.

What about the possibility that North Korea and China are playing a game of good cop / bad cop with our military planners? What if Japan is toying with the idea of leading an unholy alliance? Behind our backs? Do we really have enough Japanese-speaking spies to keep track of all the secret Samurai cults that might be conspiring at the highest levels of government. Do we?

What if Vladimir Putin thinks: The United States lied to me. I helped to elect an American president who is ineffective—a buffoon who can’t help me the way he promised. Let’s get ’em!

Imagine an alliance of China, North Korea, Russia, and Japan; an alliance led by the one country that has the greatest lust for payback; the strongest ache to settle scores once and for all.

A Hunkpapa Lakota holy man, Sitting Bull, had the vision that led to the defeat of the USA’s 7th Calvary Regiment on June 26, 1876—one week before the USA’s 100th anniversary. Five of seven battalions were decimated—one led by Civil War hero George Armstrong Custer. Sitting Bull became a celebrity who worked in Buffalo Bill’s Wild West Show. Later in life he became a leader of the Ghost Dance movement, which terrified whites, because it prophesied the exodus of white people from native American lands. Ten days before Christmas—on December 15, 1890 during an arrest by police on reservation property—Indian Affairs agents shot Sitting Bull in the head and chest in front of his family and friends. Agents removed his body to Fort Yates, where they buried him in a makeshift coffin.  

A surprise attack by such an alliance would be nation ending. It might end like the Battle of the Little Bighorn. We don’t have enough soldiers or missiles or ships to fight a gathering of tribes who possess tens of thousands of nuclear weapons.

The USA has the power to destroy the whole world if we must, but we can’t save ourselves; we can’t save our country; we can’t save the planet.

In the conflagration that took the hyper-alert Lieutenant Colonel George Armstrong Custer by surprise, all his ribbons and medals; all his accolades; all his friends in high places couldn’t save him, his men, or even his horses. The battle of the Little Bighorn was a massacre that dwarfed Custer’s reputation for being a really good person; a hero of the Civil War loved by every patriotic American.

To those who say, Billy Lee, you’ve gone paranoid on us… the Japanese would never organize an attack against America unawares… not a nuclear attack… they know how bad it would be… they suffered through one… they know better than anyone… and look at them, how they smile when we tell bad jokes. The last thing on their minds is revenge. The very last thing!

I say, you are so right!  The Japanese would never hurt us. I lived in Japan for two years after the war. The Japanese have their quirks, yes, but most of them are not cruel or insensitive. They don’t enjoy watching torture videos for entertainment, most of them. Tying up women and twisting their bodies to prepare them for rape is not something most Japanese men would have any part in. Am I right? Of course I am.

The Japanese are not monsters. They are a kind and gentle people who don’t farm or ranch or mine, because they are resource impoverished. When I lived there our Japanese house-maids and yard-boys were as sweet as they could be. They meant us no harm. I see that now. 

But how on earth are the Japanese going to get rid of the 47 tons of plutonium poison they have produced? And how will they dispose of the eight tons they plan to produce each year into perpetuity—plutonium which they admit has no longer any peacetime applications whatsoever?

Everybody knows plutonium has a radioactive half-life of 24,000 years. It’s never going to go away. Someday, through inattention or from whatever other cause, plutonium containment structures are going to rot, and the poison will leach into the soils, the oceans, and the atmosphere to kill all living things. It is Earth’s best case scenario—the scenario where nuclear war never happens, the world disarms, and plutonium is tucked away out of reach and out of sight of war makers and other terrorists.

The process that will sterilize the planet of all life is already well underway and cannot be stopped—not over a period of tens of thousands of years. Read the essay, RISK, elsewhere on this site. Humans are likely to be extinct by the time the unnatural poisons of war and opulence first make their advance against the innocent, less intelligent life-forms that we will leave behind—like chipmunks and kittens, for example—who will never be able to understand what is killing them or why.

Our new president is in Tokyo as I’m writing this essay. Anyone who asks him will learn—because he’s not afraid to say it—he is really smart and bigly educated. He understands people and how best to manipulate them to maximize his advantages and get what he wants. You don’t believe it?  Ask him—for the love of God—ask him. 

Maybe we should help the Japanese store their plutonium in a safe place—a place much safer than their earthquake tormented islands that float within the largest fisheries of the Pacific Ocean. We could store the plutonium perhaps deep in a cave somewhere. Maybe we could store it beneath the volcanic cauldrons of Yosemite—or some other remote location, like a trench astride the San Andreas fault.

Yeah, that sounds good. Let’s do that.

If we talk nicely, will the Japanese listen? Maybe they will, if our new president has the sense to ask. Does anyone have a better idea? For the love of God, tell someone. 

Billy Lee


What makes i^i interesting is the four real numbers it generates. (The numbers are +.2078… , -.2078… , +4.8104… , and -4.8104… .)

Can anyone give a geometric reason why an imaginary number raised to the power of an imaginary number generates four real numbers and no imaginary ones? What does \sqrt{-1}^{\sqrt{-1}} even mean? Is there anyone who can visualize a reason why the answers make sense? Are all the answers even correct? Or is only one correct, as any calculator that can do the calculation will tell you?

Complex numbers are two-dimensional numbers that are made by raising the number “e” to the power of an imaginary number—called “i”—times an angle in radians. Complex numbers lie on a circle in the complex number plane. Unless “e” is preceded by a number that stretches or shrinks it, the numbers lie on a unit circle like the one in the picture. Recall that “i” is the square root of minus one. When “i” is raised to the power of “i”, the result collapses onto the real number line—in one of four possible places. Which one? The numbers aren’t found on the unit circle. The process can be demonstrated mathematically, but any physical intuition about why imaginary numbers with imaginary exponents behave the way they do can be elusive.

Abstract math that hides no model that anyone can visualize makes results startling, even unnerving. It’s a lot like the quantum mechanics of entanglement or the physical meaning of gravity. They can be mathematically described and their effects accurately predicted, but no one can explain why.   

Mathematics alone can sometimes describe (or at least approximate) realities of the universe and how it seems to work, but as often as not when humans dive deep into the abyss of ultimate knowledge, math is unable to provide a picture that anyone can understand. How can that be? Things seem to happen that cannot be thought about except by playing around with numbers and being taken by surprise. Intuition is difficult, if not impossible.

Here is the solution of  i^i. Perhaps clues exist in the math that I’ve overlooked. If a model exists in the mind of a reader somewhere, I hope they will share it with me.

(1)       i^i = e^{\ln(i^i)} = e^{i\ln(i)} = cos (ln i) + i sin (ln i)

Now:  e^{i\frac{\pi}{2}} = i

Also:  ln ^{(e^{i\frac{\pi}{2})}} = ln i

Therefore:     ln i =  i (\frac{\pi}{2})

By substitution into line (1):    i^i = cos (i\frac{\pi}{2}) + i sin (i\frac{\pi}{2})

By half angle formulas:             i^i  = (\sqrt\frac{1 + cos (i\pi)}{2}) + i (\sqrt\frac{1 - cos (i\pi)}{2})

Convert 2nd term i to  \sqrt -1 :     i^i  = (\sqrt\frac{1 + cos (i\pi)}{2}) + \sqrt -1 (\sqrt\frac{1 - cos (i\pi)}{2})

(2)     Simplify the 2nd term:     i^i  = (\sqrt\frac{1 + cos (i\pi)}{2}) + (\sqrt\frac{cos (i\pi)-1}{2})

Euler’s cosine identity is:   cos θ =  \frac{e^{i\theta} + e^{-i\theta}}{2}

Therefore:                          cos (iπ) =  \frac{e^{i(i\pi)} + e^{-i(i\pi)}}{2}

(3)     Simplifying:               cos (iπ) =  \frac{e^{-\pi} + e^{\pi}}{2}

Substitute line (3) into line (2) and simplify:
i^i  = \sqrt{{\frac{1}{2} + \frac{e^{-\pi} + e^{\pi}}{4}}} + \sqrt{{\frac{e^{-\pi} + e^{\pi}}{4}} - \frac{1}{2}}

Now it’s just a matter of pulling out an old calculator and punching the keys.

e^{-\pi} = .043214;  e^{\pi} = 23.140693. I rounded off both numbers, because they seem to go on forever like π and “e”; they probably are irrational, because they don’t seem to be formed from ratios of whole numbers. Using these values will enable anyone to compute {i^i} who has a calculator with a square root key.

When square roots are calculated the answers can be positive or negative. Two negatives make a positive, right? So do two positives. So doing the math gives four numbers. See if your numbers match mine: .2078… , -.2078… , 4.1084… , and -4.1084… .  

I don’t know why. The answers aren’t intuitive. Who would guess that imaginary numbers raised to powers of imaginary numbers yield real numbers?—not a solitary number like anyone might expect, but four. Pick one. In nature a unique answer can be arbitrary—determined by chance, most likely.

In this case, no.

It feels to me like the imaginary fairies flying around in complex space are destined to collapse onto the real number line for no good reason, except that the math says they must collapse (maybe from exhaustion?) in at least one of four places. Can anyone make sense of it? 

The ln i is well known. It is i\frac{\pi}{2}, which equals (1.57078… i ). The ln of i^i can be rewritten by the rules of logarithms as i ln i, which is i times (1.57078…i ), which equals -1.57078… (a real number). Right? The ln of the correct answer must equal this number. Only one of the four results listed above has the right ln value: .2078… .

It seems odd that a set of equations I know to be sound should return a set of results from which only one can be validated by back-checking. Maybe there is something esoteric and arcane in the mathematics of logarithms that I missed during my education along the way.

Then again square roots can be messy; there are two square roots in the final equation, each of which can be evaluated as positive or negative. Together they produce four possible answers, but just one result is the right one.

Adding the four numbers is kind of interesting. They sum to zero. That is so like the way the universe seems to work, isn’t it? When everything is added up, physicists like Stephen Hawking claim, there’s really nothing here. Everything is imaginary. Some philosophers agree: everything that is real is at its core imaginary.   

Are there clues in the pictures and models of complex number space that would ever make anyone think? Sure, I totally get it. Yeah, I’ve got this. Real numbers cascading out of imaginary powers of imaginary numbers make perfect sense—like snowflakes falling from a dark sky.

A mathematician told me, Rotating and scaling is all it is. The base must be the imaginary “i” alone; “i” is the key that unlocks everything. The power of the key can be any imaginary number at all; “i” is why the result of every imaginary power of “i” becomes real. 

The explanation calms me; but it seems somehow incomplete; it’s missing something; in my gut I feel like it can’t be entirely right, though it purports to persuade what the math insists is truth. We are being asked to believe, for now at least, and move on.

Billy Lee