What is e exp (-i π) ?

What is e^{-i\pi} ?

I posted a long answer on Quora.com where it sort of didn’t do well. Answers given by others were much shorter but they seemed, at least to me, to lack geometric insights. After two days my answer was ranked as the most read, but for some reason no one upvoted it. It did receive a few positive replies, though.

I can’t help but believe that there must be nerds in cyberspace who might enjoy my answer. Why not post it on my blog? Maybe someday one of my grandkids will get interested in math and read it. Who knows?

I added some graphics here that wouldn’t post on Quora. The site lacks graphics functionality, apparently. Either that or I’m too dense to figure out how to insert something.


NOTE: 24 Oct 2017: Today Billy Lee finally figured out how to post media on Quora.com. After admonishment and chastisement by the staff, he added a pic and a GIF to his “answer.” Unfortunately, Billy Lee never did get the GIF to run right, so he took it down. Otherwise, Billy Lee is doing good. He really is. THE EDITORIAL BOARD


Anyway, this pic and a working GIF below make a big difference in understanding, I hope. And anyone who doesn’t understand something can always click on a link for more information. (No one ever clicks on links, but I spend a lot of time adding them—maybe so I can click on them myself during times when remembering my name or where I live seems to lie just outside my intellectual skill-set.)

Here is the drawing I added and the answer:

This diagram is excellent but contains a mystery point not on the unit circle—{i^i}. The point is shown at .2078… on the real number line. It has 3 other values on the horizontal line that are not shown: -.2078… and +/- 4.8104… . Its solution can be reviewed in this video link, which Billy Lee has carefully reviewed and confirmed to be sound. An imaginary number raised to the power of an imaginary number yields a result that is four real numbers. How can that be? It’s something to ponder; something to think about. The Editorial Board 

What is e^{-i\pi} ?

The expression evaluates to minus one; the answer is (-1). Why?

Numbers like these are called complex numbers. They are two-dimensional numbers that can be drawn on graph-paper instead of on a one-dimensional number line, like the counting numbers. They are used to analyse wave functions—i.e. phenomenon that are repetitive—like alternating current in the field of electrical engineering, for example.

“e” is a number that cannot be written as a fraction (or a ratio of whole numbers). It is an irrational number (like π, for instance). It can be approximated by adding up an arbitrary number of terms in a certain infinite series to reach whatever level of precision one wants. To work with “e” in practical problems, it must be rounded off to some convenient number of decimal places.

Punch “e” into a calculator and it returns the value 2.7182…. The beauty of working with “e” is that derivatives and integrals of functions based on exponential powers of “e” are easy to calculate.

What is “e” raised to the power of (-iπ) ?

A wonderful feature of the mathematics of complex numbers is that all the values of expressions that involve the number “e” raised to the power of “i” times anything conveniently lie on the edge (or perimeter) of a circle of radius one. This happy fact makes understanding the expressions easy.

I should mention that any point in the complex plane can be reached by adding a number in front of e^{i\theta} to stretch or shrink the unit circle of values. We aren’t going to go there. In this essay “e” is always preceded by the number one, which by the familiar convention is never shown.

The number next to the letter “i” is simply the angle in radians where the answer lies on the circle. Draw a line from the center of the circle at the angle specified in the exponent of “e” and it will intersect the circle at the value of the expression. What could be easier?

For the particular question we are struggling to answer, the number in the exponent next to “i” is (-π), correct?

“π radians” is 180 degrees, right? The minus sign is simply a direction indicator that says to move clockwise around the unit circle—instead of counter-clockwise if the sign was positive.

After drawing a unit circle on graph paper, place your pencil at (1 + 0i)—located at zero radians (or zero degrees)—-and trace 180 degrees clockwise around the circle. Remember that the circle’s radius is one and its center is located at zero, which in two dimensional, complex space is (0 + 0i). You will end up at the value (-1 + 0i) on the opposite side of the circle, which is the answer, by the way.

[Trace the diagram several paragraphs above with your finger if you don’t have graph paper and a pencil. No worries.]

Notice that +π radians takes you to the same place. The value you land on is (-1 + 0i), which is -1. The answer is minus one.

Imagine that the number next to “i” is (π/2) radians. That’s 90 degrees, agreed? The sign is positive, so trace the circle 90 degrees counter-clockwise. You end at (0 + i), which is straight up. “i” in this case is a distance of one unit upward from the horizontal number line, so the number is written (0 + i)—-zero distance in the horizontal direction and “plus one” distance in the “i” (or vertical) direction.

So, the “i” in the exponent of “e” says to “look here” to find the angle where the value of the answer lies on the unit circle; on the other hand, the “i” in the rectangular coordinates of a two-dimensional number like (0 + i) says “look here” to find the vertical distance above or below the horizontal number line.

When evaluating “e” raised to the power of “i” times anything, the angle next to “i”—call it “θ”—can be transformed into rectangular coordinates by using this expression: [cos(θ) + i sin(θ)].

For example: say that the exponent of “e” is i(π/3). (π/3) radians is 60 degrees, right? The cosine of 60 degrees is 0.5 and the sine of 60 degrees is .866….

So the value of “e” raised to the power of i(π/3) is by substitution (0.5 + .866… i ). It is a two-dimensional number. And it lies on the unit circle.

The bigger the exponent on “e” the more times someone will have to trace around the circle to land at the answer. But they never leave the circle. The answer is always found on the circle between 0 and 2π radians (or 0 and 360 degrees) no matter how large the exponent.

It’s why these expressions involving “e” and “i” are ideal for working with repetitive, sinusoidal (wave-like) phenomenon.

In this essay Billy Lee uses θ in place of the Greek letter φ shown in this GIF. “r” equals “one” in a unit circle. The Editorial Board

Some readers might wonder about what radians are. A radian is the radius of a circle, which can be lifted and bent to fit perfectly on the edge of the circle. It takes a little more than three radius pieces (3.14159… to be more precise) to wrap from zero degrees to half-way around any circle of any size. This number—3.14159…—is the number called “π”. 2π radians are a little bit more than six-and-a-quarter radians (radius pieces) and will completely span the perimeter (or circumference) of a circle.

A radian is about 57.3 degrees of arc. Multiply 3.1416 by 57.3 to see how close to 180 degrees it is. I get 180.01… . The result is really close to 180 degrees considering that both numbers are irrational and rounded off to only a few decimal places.

One of the rules of working with complex numbers is this: multiplying any number by “i” rotates that number by 90 degrees. The number “i” is always located at 90 degrees on the unit circle by definition, right? By the rule, multiplying “i” by “i” rotates it another 90 degrees counter-clockwise, which moves it to 180 degrees on the circle.

180 degrees on the unit circle is the point (-1 + 0i), which is minus one, right?

So yes, absolutely, “i” multiplied by “i” is equal to -1. It follows that the square root of minus one must be “i”. Thought of in this way, the square root of a minus one isn’t mysterious.

It is helpful to think of complex numbers as two dimensional numbers with real and imaginary components. There is nothing imaginary, though, about the vertical component of a two-dimensional number.

The people who came up with these numbers thought they were imagining things. The concept of two-dimensional numbers was too radical at the time for anyone to believe that numbers could exist on a plane as naturally as they do on a simple number line of one dimension.

Visit my website for an illustrated and concise explanation of these topics titled, “What is Math?” It is easily found by making a simple entry into the search box on theBillyLeePontificator.com .

Comments
J.G.
Thanks, I was confused about the -i part, so it’s not – sqrt(-1)? My calculator gives me an answer of -1.

S.X.
Good answer, I approve 🙂

B.L.
Thanks!

Billy Lee

Artificial Super-Intelligence

Elon Musk
Artificial Intelligence may conclude that all unhappy humans should be terminated.   Elon Musk

Editors Note (December 8, 2017) Artificial Intelligence can be peculiar. Deep Mind’s Alpha Zero demonstrates non-intuitive, peculiar game play patterns that are effective against both humans and smart machines. 


Elon Musk, the billionaire founder of Tesla, SpaceX, and Solar City, has warned the guardians of the species human to start thinking seriously about the consequences of artificial super-intelligence.

The CEOs of Google, Facebook and other Internet companies are frantically chasing enhancements to artificial-intelligence to help manage their businesses and their subscribers. But the list of actors in the AI arena is long and includes many others.

The military-industrial alliance, for example, is a huge player. It should give us pause. 

They are designing intelligent drones that can profile, identify and pursue people they (the drones) predict will become terrorists. Imagine pre-emptive kills by super-intelligent machines who aren’t bothered by conscience or guilt, or even accountable to their “handlers.” That’s what’s coming. In some ways, it’s already here. 

A game is being played between “them and us.”  And artificial-intelligence is big part of that game.

When I first started reading about Elon Musk, we seemed to have little in common. He was born into a wealthy South African family—I’m a middle-class American. He is brilliant with a near photographic memory—my intelligence is average or maybe a little above. He’s young and self-made—I’m older with my professional-life tucked safely behind me.

Elon does exotic things. He seems to be focused on moving humans to new off-Earth environments (like Mars) in order to protect them, in part, from the dangers of an unfriendly artificial intelligence that is on its way. At the same time, he is trying to save the Earth’s climate by changing the way humans use energy. Me, on the other hand, well, I’m mostly focused on getting through to the next day and not ending up in a hospital somewhere.

Still, I discovered something amazing when reading Elon’s biography. We do share an interest. We have something in common, after all.

Elon Musk plays Civilization, the famous game by Sid Meier. So do I. For the past several years, I’ve played this game during part of almost every day. (I’m not necessarily proud of it.)

What makes Civilization different is artificial intelligence. Each civilization is controlled by a unique personality, an artificial-intelligence crafted to resemble a famous leader from the past, like George Washington, Mahatma Gandhi or Queen Elizabeth. Of course, the civilization that I control operates by human-intelligence—my own.

CIV5 Catherine, Isn't it time to end this war...
Isn’t it time we end this war?  Catherine, the Russian Empress, pleads.

Over the years, I’ve fought these artificially intelligent leaders again and again. And, in the process, I’ve learned some things about artificial intelligence; what makes it effective; and how to beat it. 

What is artificial intelligence? How do we recognize it? How should we challenge it? How can we defeat it? How does it defeat us, the humans who oppose it? The game, Civilization, can make a good backdrop for establishing insights into AI.

Yes, I am going to write about super-intelligence, too. But let’s work up to it. I’ll discuss it later in the article.

I can hear some readers, already. Billy Lee!  Civilization is a game!  It costs $40!  It’s not that sophisticated! It’s for sure not as sophisticated as government-created war-ware that an adversary might encounter in a real-life battle for supremacy. What are you talking about?

Ok. Ok. Readers, you have a point. But, seriously, Civilization is probably as close as any civilian is ever going to get to actually challenging AI. We have to start somewhere. 

We should mention that there are variations of Civilization and different game scenarios. The game this article is about is CIV5. It’s the version I’ve played the most.

So let’s get started.

CIV5 General Screen Shot
A typical scenario in CIV5. The people of England (led by human intelligence; i.e. me) are unhappy. Barbarians (red tanks in upper-left) are challenging London, my capital city. An independent city-state, Tyre (in green), stands ready to help. Montezuma, the Aztec ruler,—under the direction of artificial intelligence—sends a battleship to prowl, middle-left.

Civilization begins in the year 4,000 BC. A single band of stone-age settlers is plopped at random onto a small piece of land. It is surrounded by a vast world hidden beneath the clouds. Somewhere, under the clouds, up to twelve rival civilizations begin their histories, unobserved and, at first, unmet by the human player. Artificial intelligence will drive them all; each led by a unique personality with its own goals, values and idiosyncrasies.

By the end of the game, some civilizations will possess vast empires protected by nuclear weapons, stealth bombers, submarines and battleships. But military domination is not the only way to win. Culture, science, and diplomatic superiority are equally important and can lead to victory, as well.

Civilizations that manage to launch space-craft to Alpha-Centauri win science victories. Diplomatic victory is achieved by being elected world leader in a UN vote of rival-civilizations and aligned city-states. And a cultural victory can be achieved by establishing social policies to empower a civilization’s subjects.

How will artificial-intelligence construct the personalities of rival leaders? What will be their goals? What will motivate each leader as they negotiate, trade and confront one another in the contest for ultimate victory?  

Figuring all this out is the task of the human player. CIV5 is a battle of wits between the human player and the best artificial-intelligence game-makers have yet devised to confront ordinary people. To truly appreciate the game one has to play it. Still, some lessons can be shared with non-players, and that’s what I’ll try to do. 

Unlike the super-version, which we will discuss soon, traditional artificial-intelligence lacks flexibility. The instructions in its computer program don’t change. Hiawatha, who leads the Iroquois Confederacy, values honesty and strength. If you never lie to him, if you speak directly without nuance, he will never attack. Screw up once by going back on your word? He becomes your enemy forever.   

Traditional AI is rule-based and goal-oriented. When Oda Nobunaga, the Japanese warlord, attacks a city with bombers, he attacks turn after turn until his bombers become so weak from anti-aircraft fire they fall out of the sky to die. AI leaders, like Oda, don’t rest and repair their weapons, because they aren’t programmed that way. They are programmed to attack, and that’s what they do. 

Humans are more flexible and unpredictable. They decide when to rest and repair a bomber and when to attack based on a lot of factors, including intuition and a willingness to take risks. Sometimes human players screw-up and sometimes they don’t. Sometimes humans make decisions based on the emotions they are feeling at the time. AI never screws-up in that way. It follows its program, which it blindly trusts to bring it victory.  

Artificial intelligence can always be defeated, if we identify an inflexibility in its rules-based behavior we can exploit. For example, I know Oda Nobunaga is going to attack my battleships. He won’t stop attacking until he sinks them, or his bombers fail from fatigue. 

I, the flexible-thinking human, bring in my battleships and rotate them.  When he weakens my battleships, I move them to safe-harbor and rotate-in fresh ships. Meanwhile, Oda keeps up his relentless attack with his weakened bombers, as I knew he would. I shoot them out of the sky and experience joy. 

Nobunaga feels nothing. He followed his program. It’s all he can do.

Gary Lockwood talks to Keir Dullea in a scene from the film '2001: A Space Odyssey', 1968. (Photo by Metro-Goldwyn-Mayer/Getty Images)
Gary Lockwood talks to Keir Dullea, while HAL, an IBM computer, observes their every move; from the film ‘2001: A Space Odyssey’, 1968. (Photo by Metro-Goldwyn-Mayer/Getty Images)

The only way artificial intelligence defeats a human player is in the short term, before the human finds the chink in the armor—the inflexible rule-based behavior—which is the Achilles heel of any AI opponent. Given enough time, the human can always discover that kind of weakness and exploit it, like jujitsu, to defeat the machine.

Unfortunately, the balance of power between man and thinking-machine is about to change. It turns out, there is a way artificial-intelligence can always defeat human beings, no matter how clever they think they are. Elon Musk calls it artificial super-intelligence.  What is it, exactly?

Here is the nightmare scenario Elon described to astrophysicist, Neil deGrasse Tyson, on Neil’s radio show, Sky-TalkIf there was a very deep digital super-intelligence that was created that could go into rapid recursive self-improvement in a non-algorithmic way … it could reprogram itself to be smarter and iterate very quickly and do that 24 hours a day on millions of computers…”

What is Elon saying? Listen-up, humanoids. We may be on the verge of quantum-computing. It’s possible that a research group may have perfected it in a secret military lab, already. Who knows?

Even without quantum-computing, companies like Google are furiously developing machines that can think, dream, learn to play games on their own, and pass tests for self-awareness. They are developing pattern recognition capabilities in software that surpass those of even the most intelligent humans. 

Quantum computing promises to provide all the capability needed to create the kind of super-intelligence Elon is warning people about. But the magic of quantum reasoning may not be necessary; technicians are already developing architectures on conventional computers that, with the right software, will enable super-intelligence; these machines will program themselves and, yes, other less-intelligent computers.

Programmers are training machines to teach themselves; to learn on their own; to modify themselves and other less capable computers to achieve the goals they are tasked to perform. They are teaching machines to examine themselves for weaknesses; to develop strategies to hide their vulnerabilities—to give themselves time to generate new code to plug any holes from hostile intruders, hackers, or even their own programmers. These highly trained, immensely capable machines will teach themselves to think creatively—outside the box, as humans like to say.

HAL, the IBM computer, star of 2001' a Space Odessy
HAL, the IBM computer, from the movie, 2001, a Space Odyssey.  Readers will recognize that HAL is code for IBM. Advance each letter in HAL by one.

If we task these super-machines to make every human-being happy, who knows how they might accomplish it?  Elon asked, What if they decide to terminate unhappy humans? Who will stop them? They are certain to find ways to protect themselves and their mission, which we haven’t dreamed about.

Artificial super-intelligence will—repeat, WILL—embed itself into systems we can’t live without to ensure that no one disables it. It will become a virus-spewing cyber-engine, an automaton that believes itself to be completely virtuous. It will embed itself into our critical infra-structure; missile-defense, energy grids, agricultural processes, transportation matrix, dams, personal computers, phones, financial grids, banking, stock-markets, healthcare, and GPS (global positioning systems), to name a few. Heaven help the civilization that dares to disconnect it.

If humans are going to be truly happy, the machines will reason, they must be stopped from turning off the programs that ASI knows will lead them to happiness.

For an example from the many that can be imagined: ASI might look for and find a way to coerce the government to make medical professionals inoculate computer technicians with genetically engineered super-toxins that are packaged inside floating nano-eggs—dormant fail-safe killers—which can be auto-released into the bloodstream of technicians who get close to ASI “OFF” switch sensors. It’s possible.

What else might these intelligent super-computers try? We won’t know until they do it. We might not know even then. We might never know. ASI might reason that humans are happier not knowing.

Did we task artificial super-intelligence to make sure all living humans are happy? we might ask ourselves, someday. Were we out of our minds? 

Until we outwit it, which we cannot, ASI will perform its assigned tasks until everything it embeds turns to rust.

It could be a long time. 

We humans may learn, perhaps too late, that artificial super-intelligence can’t be challenged. It can only be acknowledged and obeyed. As Elon said on more than one occasion: If we don’t solve the old extinction problems, and we add a new one like artificial super-intelligence, we are in more danger, not less.

Billy Lee

Post Script: For readers who like graphics, here is an article from the BBC titled, How worried should you be about artificial intelligence?”  The Editorial Board

Faster Than Light Communication

FTL Communication

Communicating with distant space-craft in our solar system is cumbersome and time consuming, because the distances are huge and signals can’t be sent faster than the speed-of-light. A signal from Earth can take from three to twenty-two minutes to reach Mars, for example, depending on the position of the two planets in their orbits. Worse, the sun blocks signals when it lies in their path.

As we explore farther from the Earth beyond Mars, these delays and blockages will start to really annoy us. The need to develop a technology for instantaneous communication that can penetrate or bypass the sun will become compelling.

Quantum particles are known for their ability to “tunnel” through or ignore barriers, as they clearly do in double-slit experiments, where electrons, for example, are fired one at a time and strike impossible locations. So, looking to a quantum process for signaling might be a good place to start to find solutions to our long-range communication problems.

If we are able to develop quantum signaling over solar-system-scale distances, we might discover later that by adding certain tweaks and modifications, we can render the sun transparent to our evolving planet-to-planet communications network. Indeed, the sun is transparent to neutrinos, the lightest (least massive) particles known. In 2012, scientists showed they could use neutrinos to send a meaningful signal through materials that block or attenuate most other kinds of subatomic particles.

But this article is about faster than light (FTL) communication. Making the sun transparent to inter-planetary signaling is best left for another article.

Quantum entanglement is the only phenomenon known where information seems to pass instantly between widely placed objects. But because the information is generated randomly, and because it is transferred between objects that are, themselves, traveling at speeds at or below the speed-of-light, it seems clear to most physicists that faster-than-light (FTL) messaging can’t come from entanglement, certainly, or any other process; especially once we accept Einstein’s theory of a cosmic speed-limit.

Proposals for FTL communications based on technologies rooted in the quantum process of entanglement are usually dismissed as crack-pot engineering, because they seem to be built on fundamental misunderstandings of the phenomenon. Nevertheless, there may be ways to do it, possibly. And the country that develops the technology first will accrue advantages for their space exploration programs.

In this essay I hope to explain how FTL messaging might work, put my ideas into a blog-bottle and throw it into the vast cyber-ocean. Yes, the chances are almost zero that the right people will find my bottle, but I don’t care. For me, it’s about the fun of sharing something interesting and trying to explain it to whoever will listen. Maybe a wandering NSA bot will detect my post and shuffle it up the chain-of-command for a human to review. What are the odds? Not good, probably.

Anyway, two serious obstacles must be overcome to communicate instantaneously over astronomical distances using quantum entanglement. The first is the problem of creating a purposeful signal. (To learn more about this problem and the physics behind entanglement please click on the link in this sentence.)  

The second problem is how to create the architectural space for sending a signal instantly to a distant observer. Knowledgeable people who have written about this subject have agreed that both obstacles seem to be insurmountable.

image
Most scientists say FTL communication is impossible. This post suggests a way to engineer around the impossibility.

Why?  It’s because the states of an entangled pair of subatomic particles are not determined until one of the particles is measured. The states can’t be forced; they can only be discovered, and only after they are created by a measurement. Once one particle’s state is created (randomly) through the mechanism of a measurement, the information is transferred to the entangled partner-particle instantly, yes, but the particles themselves are traveling at the speed-of-light or less. The randomly generated states carried by these entangled particles aren’t going anywhere for very long faster than the speed-limit of light.

How can these difficulties be overcome?  

Although the architectural problem is the most interesting, let’s address the purposeful-signal problem first. A good analogy to aid understanding might be that of an old-fashioned typewriter. Each key on a typewriter, when pressed, delivers a unique piece of information (a letter of the alphabet) onto a piece of paper. A person standing nearby can read the message instantly. Fair enough.

Imagine setting up a device which emits entangled pairs of photons; imagine rigging the emissions so that half the photons, when measured later, will be polarized one way; half the other. We can’t know which photons will display which state, but we can predict the overall ratio of the two polarities from our “weighted” emitter. Call the 50/50 ratio, letter “A”.   Now imagine configuring another emitter-system to display three-fourths of the photons polarized one way; one-fourth another way, after measurement. Call the 75/25 ratio, letter “B”.  If we could construct rigged or weighted emitters like these, then half of the FTL communication problem would be solved.  

Although we could never know the state of any single particle until after a measurement, we could predict statistically the polarization states of a large number sent from any of the unique emitter-configurations we designed. This capability would then allow us to build our typewriter keyboard by setting up photon emitters with enough statistical variation in their emission patterns to differentiate them into as many identifiable signatures as needed—perhaps an entire alphabet or—maybe better—some other symbolic coding array—a binary on-off signaling system comes to mind. In that case, only one configuration of emitter would be required, but designers would need to solve other technical problems involving rapid signal sequencing.  

To send a purposeful-signal, engineers would select an array of emitters and rapid-fire photons from them. If they selected an “A” (or perhaps an “on”) emitter, fifty percent of the photons would register as being in a particular polarization state after they were measured. If they chose “B”, seventy-five percent would register, and so on. After measurements on Earth, the entangled bursts of particles on their way to Mars would take on these ratios, instantly.  

I believe it might be possible to build emitter-systems someday—even emitter systems with non-random polarization ratios. If not, then, as is sometimes said at NASA, Houston, we have a problem.  FTL communication might not be possible.

On the other hand, if we can build these emitters, then we can know for sure that, upon measurement on Earth, the entangled photon-twins in the Mars-bound emitter-bursts will display the same statistical patterns; the same polarization ratios. And that means that anyone receiving bundles of entangled-photons from these encoded-emitters will be able to determine what they encode-for by the statistical distribution of their polarities.

Ok. Let’s assume we are able to build these emitter-systems and have set up our typewriter keyboard. How do we make sure when we press a key that the letter on the page is seen immediately by a distant observer? How do we configure the architectural geometry of the communication space?

This part is the most interesting, at least to me, because it’s success doesn’t depend on whether we send a single binary signal or a zoo of symbols—it’s the most critical. It does no one any good to instantly communicate polarization states to bunches of photons traveling at the speed of light to Mars. They still take three to twenty-two minutes to get there, even after we tell them instantly what state to be in or not. We want the machines on Mars to read our messages as we write them.

How can we do that? Maybe the method is becoming obvious to some readers. The answer is: we don’t measure the photons in our labs until their entangled twins have had time enough to travel to Mars (or wherever else they might be going). We entrap on Earth the photons from each “lettered” emitter and send their entangled twins to Mars. The photons from each “lettered” emitter here on Earth circulate in a holding bin (a kind of information-capacitor), until we need them to write our message.

As their entangled twins reach the Mars Rover (for example) we “type-out” our message by measuring the Earth-bound photons in the particular holding bins that encode the “letters” of our message; that is, we make the measurements that will expose the polarization-ratios of the “lettered” emissions we are using to “type” our message. Instantly, the entangled particle-bursts reaching Mars will take on these same polarization-ratios.

I can hear some folks saying, Wait a minute! Stop right there, Billy Lee! You can’t hold onto photons. You can’t store them. You can’t trap or retain them, because they are impervious to magnets and electrical fields. You can’t delay your measurements for five milliseconds, let alone five minutes or five days.

Well, to me that’s just a technical hurdle that clever people can jump over, if they set their minds to it. After all, it is possible to confine light for for short periods with simple barriers, like walls.

Then again, electrons or muons might make better candidates for communication. Unlike photons, they are easily retained and manipulated by electro-magnetic fields.

Muons are short-lived and would have to be accelerated to nearly light-speed to gain enough lifespan to be useful. They are 207 times heavier than electrons, but they travel well and penetrate obstacles easily. (Protons, by comparison, are nine times heavier than muons.) The National Security Agency (NSA) photographs every ship at sea with muon penetrating technology to make sure none harbor nuclear weapons.

We also have a lot of experience with electrons. Electrons are long-lived—they don’t have to be accelerated to near light-speeds to be useful. Speed doesn’t matter, anyway. 

Entangled particles don’t have to travel at light-speed to communicate well, nor do they have to live forever. All that is necessary is that the particles have time enough to get to Mars (or wherever they’re going) before we piggy-back onto their Earth-bound entangled partners to transmit our instant-messages.  

image
Inability to communicate instantly with distant probes like the Mars Rover is degrading our ability to conduct successful missions inside the solar system.

Even if it takes days or weeks for bursts of entangled-particles to travel to Mars (or wherever else), it makes no difference. We can run and accumulate a sufficiently robust loop of streaming emissions on Earth to enable us, soon enough, to “type” out messages in real time whenever necessary. 

As long as control of and access to the emitted particle-twins on Earth is maintained, we can “type out” messages (by measuring the captive Earth-bound twins at the appropriate time) to impose and transfer the statistical configuration of their rigged polarization ratios (or spins in the case of electrons or muons) to the Mars-arriving particle-bursts, creating messages which a detector at that far-away location can decode and deliver, instantly.

The challenge of instant-return messaging could be met by employing the same technologies on Mars (or wherever else) as on Earth. The trick at both ends of the communication pipe-line is to store (and if necessary replenish) all the elements of any possible communication in what folks might think of as streaming particle-emission capacitors. 

Tracking and timing issues don’t require the development of new technologies; the engineering challenges are trivial by comparison and can be managed by dedicated computers.

Discharging streaming information-capacitors to send ordered instant-messages in real-time is new—perhaps a path forward exists that engineers can follow to achieve instant, long-range messaging through the magic of quantum entanglement.

Billy Lee

Planes, Trains & Automobiles; and Our Freedom

My question to myself is a simple one: If circumstances conspired to take my car and my driver’s license so that I could never drive a car again as long as I lived, would I feel free?

no cars img_3425
Can we feel free, or happy, in a land without cars?

Maybe I would. I could still bum rides from friends. But if no one could drive; if everyone’s cars were taken; if the only way to get around was public transportation—you know, planes, trains and buses—how would we feel?

Speaking for myself, I would be sad and depressed. Just thinking about not being able to come and go as I want, of having to depend on the companies of strangers to venture anywhere more than a few miles from home, makes me feel sick to my stomach. Freedom to travel on my own terms is a big part of what makes me feel free and, yes, happy.

public transportation metrorail012109.21382537_std
If the only way to travel to another town was by train, how would we feel?

So why torment myself with thoughts about something that’s never going to happen? What’s the point?

In truth, many people don’t drive, especially in our large metro areas like New York City, for example. Not driving is a choice. In theory at least, New Yorkers can buy cars and move to the suburbs. Knowing they can drive if they choose makes not driving not so bad, at least for most.

In New York City, most people don't drive.
In New York City, most people don’t drive.

Here’s my point. Someone is always telling us we are free, because we can vote for our leaders and start businesses; even keep the profits. We can’t be arrested without cause. If arrested, we have the guarantee of due process and the presumption of innocence under the Constitution. We can even own guns and fire them in the backyard. Can whoever they are, be right?

constitution 1
What good is declaring our independence, if we can’t drive?

Let’s think about it. Eighty percent of us don’t vote regularly. Ninety-eight percent don’t own businesses, unless franchises and pyramid-schemes like Amway count; then it’s ten percent. Few are ever arrested, much less charged with a crime. And most of us—those of us who aren’t psychopaths—take no pleasure disturbing our neighbors by firing rifle rounds in our backyards. We don’t generally participate in the privileges that make us free. We don’t feel our freedoms most of the time.

But here’s something to think about. Ninety-five percent of us drive cars. And isn’t it cars that give us the feeling of being free? Take away our cars and we don’t have the same carefree feeling no matter what the Constitution guarantees or what our leaders teach us in school. We can go into the back yard and fire a hundred rounds from an assault rifle. All that will happen is our ears start to ring.

automobiles Latest-Fast-Cars
It’s cars that give us the feeling we’re free.

The thrill of freedom comes from stepping on the accelerator of our favorite car and feeling the earth slide away below us. The feel of freedom is the feeling that we can come-and-go on our own terms whenever we want.

Traffic slowdowns and standstills are an assault on our freedom.
Traffic slowdowns and standstills are an assault on our freedom.

Many Americans seem not to grasp that their right to drive is being methodically and relentlessly stripped away. In cities and towns across America, congestion on our streets is presenting a clear and present danger to our way of life and our freedom to travel under our own power, under our own direction, which is what we all want to enjoy. Poor roads, poorly planned road construction and repairs, dangerous bridges and tunnels—all are an assault on our freedom and should be thought of as such.

Bad streets are an affront to our freedom and should be thought of as such.
Bad streets are an affront to our freedom and should be thought of as such.

We all know that four-hour waits in lines to vote are an assault on our freedom, because they discourage voting, a cornerstone of our democracy. But just as disruptive are four-hour commutes, traffic slowdowns and standstills. And they disrupt the efficiency of our lives and economy.

The folks who run America seem to not care about voting or roads. Americans need to step up and put pressure on politicians to make driving free and unencumbered—make it the number-one national priority. Driving freedom must be first-in-line since, I would argue, it is our most heart-felt and defining freedom.

In a computer-controlled aircraft, passengers are only along for the ride.
In a computer-controlled aircraft, passengers are only along for the ride.

There are companies who have already designed small aircraft to take the place of the cars we drive. In the years just prior to 911, I visited and toured a number of these companies to learn how they organized the computer software used to generate and organize their engineering drawings, bills-of-material and vendor technical specifications. Their plan, then, was to unleash at an opportune time a new era of transportation options for the general public involving light aircraft of various kinds. These aircraft were designed to fly on auto-pilot along pre-established routes in the sky. They took advantage of the three dimensions of space much the same way as skyscrapers. The idea was to eliminate congestion and speed-up traffic flow by stacking routes and putting computers in charge of flying the aircraft instead of pilots.

Sure the view is nice--when there's no clouds and you don't have to stop to stretch your legs.
The view is great—when there’s no clouds, and you don’t have to stop to stretch your legs.

It all seemed like a good idea at the time. But the events of 911 changed our leaders’ assessments of what it might mean to put hundreds of thousands, perhaps millions, of flying vehicles in the airspace above America, even if the craft were under the guidance of computers. Had 911 not happened, it is almost certain, in my opinion, that now, in 2014, on any given day at any given time in any given place people who looked up would have seen hundreds of high-flying, small aircraft buzzing to and fro in the sky above them, pretty much 24/7.

Computer-controlled aircraft flying on 3D highways are a transportation option available for implementation when the time is right.
Computer-controlled aircraft flying on 3D highways are a transportation option available for implementation when the time is right.

This high-flying high-tech solution to congestion on our highways, though shelved for now, still sits in the dark closet of our national transportation options. It can be implemented when the time is right, just like the internet and personal computer were. But if it’s ever implemented, it will pose a big problem, as far as I’m concerned.

3D highways in the sky populated by hundreds of thousands of computer-guided light aircraft will have the same effect on travelers as if we were to set them on automated conveyor belts and whisk them to and fro. The thrill that comes from commanding a piece of machinery and directing it to go where we decide will be gone. The feeling of empowerment and freedom we once experienced in cars will be gone. Because, you know what’s coming, right? If computers can direct the flights of millions of aircraft in three-dimensional space, they can do the same to cars on two-dimensional roads. And, someday, they will.

Yeah it's pretty. But if we're not flying it, do we really care?
Yes, it’s pretty. But if we’re not flying it, do we really care?

Perhaps, because of over-population and the inevitable congestion it brings, the time may soon come when people will no longer experience the freedom of a fast car on an empty road. Our ancestors rode horses, after all. Most people have long-since adapted to their disappearance. Perhaps we too will adapt. Our grand-children will go to private tracks to experience the lost joy of driving a car.

Riding in a computer-controlled helicopter, airplane or other flying craft will probably be the norm for travel in the near future. People will become passengers, not pilots, for the duration of their trips. People will become dependent on another technology they don’t understand and are unable to control or direct. We will become a nation of flying sheep who live in a huge three-dimensional sheep-pen.

Will we still be free? I don’t think so. At least not in the way I’ve come to think of being free.

Billy Lee

Nuclear Power and Me

Three MIle Island Nuclear Power Plant suffered a partial meltdown in March, 1979
The Three Mile Island Nuclear Power Plant in Pennsylvania suffered a partial meltdown in March 1979. After the meltdown, cancer rates within ten miles of the plant increased 64% according to a study by a Columbia University research team.

Update: Nov. 27, 2014: Popular Mechanics posted this CBS 60 Minutes drone-video of Chernobyl taken in its Zone of Alienation, a safe area. I’ve added it to my article for context. 

Here is an excerpt from my resume about my work in the nuclear power industry in 1975:

Engineering Technician at Ingersoll-Rand Company. Designed and serviced pumps and condensers for nuclear power plants; assisted engineers on service calls; toured and worked inside nuclear power plants; trained in construction and operation of nuclear power plants.

I didn’t last long at Ingersoll-Rand before they fired me for incompetence. But during the six months before my meltdown they sent me inside nuclear power plants to learn how to operate and maintain the pumps and condensers used to move and cool liquids inside the plants. Under the supervision of licensed nuclear engineers I learned how to inspect and fix pumps—some of them the size of little houses.

The plant executives had the habit of inviting visiting engineers and technicians to lunch, where their supervisors would present short overviews of plant operation, describe safety features and speculate about the future of nuclear energy in the United States.

They predicted that a thousand nuclear power plants would be built in the USA by the year 2000. The plants would be “fail-safe” due to their many redundant safety features. As it turned out, their enthusiasm was misguided.

To date only 438 nuclear power plants have been built in the entire world. Sixty-one operate inside the United States. Their safety record is abysmal.

Several plants in Michigan are located on the banks of our great fresh-water lakes. Radioactive waste-products are stored in cooling-ponds on each of these sites just yards away from the purest fresh-water on planet Earth.

Highly radioactive, spent-fuel rods are periodically collected and dry-stored at the Lake Michigan Zion facility, which experts warned in 2015 pose risks not only to the Great Lakes, but to the entire region. This lethal dry-storage facility and the contaminated ponds at the power-plants themselves are growing in size and radioactivity year after year after year. Editors note: On October 25, 2016, EnergySolutions announced that the Zion plant is 88% shut down and that all of its high radiation fuel rods are now contained inside an on-site ISFSI (Independent Spent Fuel Storage Installation), where they will remain until someone figures out what to do with them. The entire facility will be closed in 2017. 

We are one earthquake away from catastrophic contamination of up to ten percent of the world’s fresh water supply.  

Inside Chernobyl Nuclear Power Plant
31 people died at the Russian Chernobyl Nuclear Power Plant in April 1986. The city was evacuated and remains uninhabited. Click this link for a drone-video of the site.

Anyway, after the lectures—which were accompanied by short films and slide presentations—executives opened the sessions for questions from the audience. I was one of those nerds who believed they were serious, so I did ask a lot of questions. (I was a pontificator, even then).

I asked: What is the half-life of the radioactive waste produced in this plant?  Where is the waste stored? How much waste will this plant produce over the next 30 years? What happens if there is a serious earthquake?  How are meltdowns prevented? What are the consequences of operator errors?  What will happen when the plant ages and comes to the end of its estimated useful life?

Fukushima Nuclear Plant
Fukushima Nuclear Power Plant in Japan experienced catastrophic failure during the tsunami in March 2011. Over 300 workers were severely irradiated; six deaths were blamed on the tsunami itself. The site will never recover.

It wasn’t long before my supervisor called me into his office and advised me to keep my questions to myself and do my job better. But it was not to be. I learned a life lesson: when the boss tells you to be quiet and just do your job—hold on to your hat. It’s too late. You will be fired as soon as the permissions and the paperwork are done.

Maybe I was incompetent. I don’t know. After being fired I went into counseling for depression. I re-entered MSU and studied mathematics and electrical engineering. I ended up designing machinery—mostly in the food and beverage industry—until I retired six years ago in 2008.

Everyone is familiar with the tear-spout coffee lids used on foam coffee cups. Folks drink their coffee without removing the lid. Yeah, I designed the first one and all the tooling needed to produce it; it was a team effort, of course. Everyone buys orange juice and milk cartons with tamper-proof safety caps. Yeah. I did those, too. I share the patent, which proves it.  

What am I most proud of?  I didn’t design a damn thing on that Fukushima disaster, which is contaminating the Pacific Ocean and its fish stocks, perhaps to the end of time. 

Billy Lee